1 Introduction

Bamboo is a tree-like plant that grows rapidly and abundantly. It has traditionally been used for fabrication of village houses, furniture manufacture and daily necessaries, without fully exploiting its potential as an engineering material (Shin et al. 1989). The modern processing techniques of bamboo have further extended its use in recent years. Bamboo-based composites such as plywood (Chen 1985), fiberboard (Matsumoto et al. 2001), oriented strand board (OSB) (Febrianto et al. 2012), oriented strand lumber (OSL) (Malanit et al. 2011), and parallel strand lumber (PSL) (Ahmad and Kamke 2011) have been carried out.

However in general, bamboo culm is a thin-walled hollow cylinder separated with nodes (Obataya et al. 2007). In order to obtain flat strips, the external and internal parts of bamboo pieces must be removed (Anwar et al. 2009). Flattening technique is a promising way to raise the utilization rate of bamboo, and it is attracting increasing attention. However, the researches and reports in this field are very limited. Mori (1987) developed a flattening process of bamboo pieces which used microwave heating. Zhang (1988) studied a flattening technique which softened bamboo by using chemical reagent.

In this study, a new theory of bamboo stressed flattening is produced and this process is experimentally examined. When a bamboo piece is flattened, its stiff outer layer is compressed while the softer inner layer is strained. Therefore, the inner layer of bamboo may easily develop cracks, or even fracture. In the process of bamboo stressed flattening, a pair of horizontal loads is exerted on both sides of the bamboo piece to counteract the tensile stress of the inner layer in response to flattening. As long as the stress of inner layer is always kept smaller than its allowable value, the purpose of non-split flattening could be reached.

2 Theoretical models

Under the stressed flattening conditions, a bamboo piece bears the resultant force of vertical load F V , a pair of horizontal loads F H and support constrained forces F A and F B (F A  = F B  = F V /2) (Fig. 1).

Fig. 1 Abb. 1
figure 1

Loading situation of bamboo piece in stressed flattening process

Lasten beim Flachpressen von Bambusproben

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In the case of the ratio of the curvature radius and arc height of a curved beam being smaller than 5, the curved beam formula should be used to calculate the circumferential stress of the beam (Hibbeler 1991). Obviously, the bamboo pieces in the present study match this condition.

If r represents the position of any micro-area unit, dA, on the cross section of bamboo piece, one has

$$ \int \limits_{A} \frac{dA}{r} = a \cdot \ln \frac{{r_{1} }}{{r_{2} }} $$
(1)

where a is the length of bamboo piece, r 1 is the external radius, and r 2 is the internal radius. Then the neutral axis, R, can be expressed as

$$ R = \frac{A}{{\int_{A} \frac{dA}{r} }} $$
(2)

where A is the cross sectional area of bamboo piece, A = a(r 1 − r 2). Thus the maximum bending moment, M max, that the bamboo piece can bear is

$$ M_{\hbox{max} } = \frac{{Ar_{2} \sigma_{b} \left( {\overline{r} - R} \right)}}{{R - r_{2} }} $$
(3)

where σ b is the transverse tensile strength of bamboo, and \( \bar{r} \) is the distance from the center of bamboo arc to the centroid of cross section, \( \overline{r} = {{\left( {r_{1} + r_{2} } \right)} \mathord{\left/ {\vphantom {{\left( {r_{1} + r_{2} } \right)} 2}} \right. \kern-0pt} 2} \).

The cross section can be simplified to arc AB of radius r 2 , as presented in Fig. 2. Point C represents the vertex of arc AB. CD is perpendicular to AB. Let the arc height CD = h (initial height is h o ), arc AC = S and AD = L.

Fig. 2 Abb. 2
figure 2

Calculation diagram of bamboo piece

Ansatz der Lasten, die auf eine Bambusprobe wirken

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For an arbitrary point on arc AB, the vertex suffers the maximum moment. The force analysis of point C can give,

$$ M_{C} = \frac{{F_{V} }}{2} \times L - F_{H} \times h $$
(4)

where M C must be kept smaller than M max from Eq. (3). Thus,

$$ \frac{{F_{V} }}{2} \times L - F_{H} \times h \le M_{\hbox{max} } $$
(5)

For the parameter of L in Eq. (5), an approximation of Arc AC = AC can be used to simplify the calculation. So,

$$ L = \sqrt {S^{2} - h^{2} } $$
(6)

Substituting Eq. (6) for L and Eq. (3) for M max into Eq. (5) gives the relationship between F H , F V and h.

$$ F_{H} \ge \frac{{F_{V} }}{2h}\sqrt {S^{2} - h^{2} } - \frac{{Ar_{2} \sigma_{b} \left( {\overline{r} - R} \right)}}{{h(R - r_{2} )}},\quad \,h \in \left( {\left. {0,h_{o} } \right]} \right. $$
(7)

Hence the range of F H that satisfies the balancing of stresses can be determined from F V and h according to Eq. (7).

3 Materials and methods

3.1 Materials

Four-year-old moso bamboo (Phyllostachys pubescens) was collected from Anhui province, China. First of all, the bamboo culms were crosscut into three portions (top, middle, basal) in their longitudinal direction. The external diameter at the top was about 65–80, 70–90 mm in the middle and larger than 85 mm at the base. Then, these three portions of bamboo were cut into 250 mm long tubes and subsequently sliced into one-third circumference bamboo pieces. Finally, each portion of pieces was assigned equally into six groups according to their external diameters (a total of 18 groups of the three portions). For bamboo pieces with nodes, the nodes should be removed and the surfaces be smoothed additionally. Prior to the following flattening tests, all these samples were soaked in water until saturation.

3.2 Devices

A manual hot-press and a special device constructed according to the stressed flattening theory were used in the test (Fig. 3).

Fig. 3 Abb. 3
figure 3

Schematic illustration of bamboo stressed flattening device

Schematische Darstellung des Spezialgeräts zum Flachpressen von Bambus

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The device which has a dimension of 48 cm in length and 30 cm in width mainly consists of three parts: the worktable, auxiliary heater and a pair of preheaters. The preheaters are used to preheat bamboo before flattening and their curved surfaces can make the heating more uniform. Each extremity of a bamboo piece is maintained by two different baffles on the worktable. The first one is fixed by a manual adjustment screw and the second one is limited by a set of horizontal springs. The value of the horizontal loads can be calculated by measuring the compression length of the springs and controlled by rotating the adjustment screw. In addition, the auxiliary heater is fitted under the bamboo piece to heat the inner surface of bamboo and its position follows the movement of displacement of bamboo arc throughout the flattening process. When the bamboo piece was completely flattened, the top of the auxiliary heater would be flush with the worktable.

3.3 Stressed flattening process

3.3.1 Loads calculations

The range of the horizontal loads should be calculated before flattening and a numerical example is shown as follows:

The bamboo piece of 1/3 round is 250 mm in length, 50 mm in diameter and 10 mm in thickness. The parameters of half the arc length, S, and the initial arc height, h o , can be calculated by the geometrical relationship of circle, thus

$$ S = \left( {50\,{\text{mm}} - 10\,{\text{mm}}} \right) \times {\pi \mathord{\left/ {\vphantom {\pi 3}} \right. \kern-0pt} 3} = 41.9\,{\text{mm}} $$
$$ h_{o} = \left( {50\,{\text{mm}} - 10\,{\text{mm}}} \right) \times \left( {1 - \cos \,{\pi \mathord{\left/ {\vphantom {\pi 3}} \right. \kern-0pt} 3}} \right) = 20\,{\text{mm}} $$

Additionally, the transverse tensile strength of bamboo in the flattening condition of 180 °C and 40 % moisture content was 4.0 MPa. Substituting the parameters above into Eq. (7), the range of applied horizontal loads, F H can be obtained. The value of F H was determined by the vertical load, F V , and the arc height of bamboo piece, h. Their relations are presented in Fig. 4.

Fig. 4 Abb. 4
figure 4

Relationships between F H , F V and h

Beziehungen zwischen F H , F V und h

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100 N was used as the smallest unit of force to simplify the operation. The pressure of hot-press, F V , was selected according to the empirical data of preliminary experiments and the whole flattening process could be divided into three stages as presented in Fig. 4. If the initial value of F V was set equal to 1,600 N, a corresponding horizontal force, F H , of 1,100 N was needed. At the beginning, F V was kept constant and F H would increase to the maximum value of 1,900 N as h decreased to 10 mm (arrow 1). Then, h decreased from 10 to 4 mm, the value of F V gradually reduced to 700 N, and the value of F H was synchronously reduced from 1,900 N to 0 (arrow 2). At last, F V was kept at the constant value of 700 N and F H was no longer needed in the remaining flattening process (arrow 3).

3.3.2 Bamboo flattening

The stressed flattening process was carried out on the device described in Fig. 3. It had two main phases: bamboo softening and bamboo flattening. Furthermore, it included a post-treatment phase which decreases the spring back of bamboo.

In the softening phase, the hot-press, preheaters and auxiliary heater were first heated to 180 °C. Then a bamboo sample was placed on the worktable, preheated for 3–4 min. After that, the preheaters were removed. In the following phase, the sample was clamped between the baffles and the initial horizontal forces required were exerted by rotating the adjustment screw. Then the hot-press was closed slowly and gently. Subsequently, the horizontal forces should be continuously adjusted as the height of bamboo piece and the pressure of hot-press changes until the sample was completely flattened. After the flattening phase, the sample should be compressed and heated for an additional 2 min to eliminate the internal stress in response to deformation. Figure 5 illustrates a flattened bamboo strip.

Fig. 5 Abb. 5
figure 5

External surface (a) and internal surface (b) of a flattened bamboo strip

Außenschicht (a) und Innenschicht (b) einer flachgepressten Bambusprobe

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3.3.3 Data analysis

The process results were characterized by some different parameters which concerned two initial states (AD—the average external diameter; AT—the average thickness) and three final states (NFLR—non-crack flattening ratio; CFLR—cracked flattening ratio; FR—fractured ratio) of each group of samples. Non-crack flattening refers to no cracks developed in the flattened bamboo strip and it is the best flattening result. Cracked flattening means that although some cracks occurred in the strip, the maximum depth of the cracks was lower than 1/2 thickness of the strip. It is also regarded as a successful flattening result. But if the maximum depth exceeded 1/2 thickness or the bamboo piece was split into halves during the test, this condition is defined as fracture which was a result of failure. In addition, the crack degree was quantified by the total length and the maximum depth of cracks. The three parameters of the final states were calculated from the following equations:

$$NFLR\:\left( \% \right) = \frac{{{\text{Amount}}\,{\text{of}}\,{\text{non}} - {\text{crack}}\,{\text{samples}}}}{{{\text{Amount of samples}}}} \times 100 $$
(8)
$$ CFLR\;\left( \% \right) = \frac{\text{Amount\,of\,cracked\,samples}}{\text{Amount of samples}} \times 100 $$
(9)
$$ FR{\kern 1pt} \;\left( \% \right) = \frac{\text{Amount\,of\,fractured\,samples}}{\text{Amount of samples}} \times 100 $$
(10)

4 Results and discussions

A total of 108 bamboo samples (36 samples for each of the three portions) were tested in this experiment. The ratios of the flattening results are presented in Table 1. Crack degree was evaluated by the total length and the maximum depth of cracks, and the average values of these two parameters were calculated for each portion of bamboo strips (Fig. 5).

Table 1 Tab. 1 Ratios of fracture, cracked flattening and non-crack flattening of 1/3 circumference bamboo samplesAnteil an bei der Flachpressung gebrochenen, angerissenen und nicht gerissenen Bambusproben, die 1/3 des Halmumfangs umfassen
Full size table

It can be seen that the flattening results of the three portions were markedly different. The middle portion had the best result in this test. It had the highest NFLR, the lowest FR, and its flattening ratio (NFLR + CFLR) reached 86.1 %, as presented in Table 1. Moreover, the middle position showed the shortest total length and the smallest maximum depth of cracks (Fig. 6). Several possible reasons might explain this result. Zhou (1981) found that the middle culms of bamboo performed better mechanical properties than other parts such as bending strength and cleavage strength. Additionally, their larger ratio of diameter and culm-wall thickness can help to reduce the internal stress in response to deformation. From the standpoint of bamboo culm form, the middle portion is straighter and its taper angle of the conical section is smaller. These characteristics will make the stress distribution on bamboo pieces more evenly. In contrast to the middle portion, the top had the highest FR, the lowest NFLR and a flattening ratio of 69.5 % (Table 1). In addition, the top portion showed the longest total length and the largest maximum depth of cracks, as illustrated in Fig. 6. This can be explained by the fact that the culms of top portion have the shortest diameter and a relatively larger scope of irregular surface. Therefore, the samples would easily create local stress concentrations on their inner surfaces as observed by Qian and Ye (1999). As shown in Table 1, the flattening ratio of basal portion was 80.6 %, a little lower than that of the middle portion. There are two possible reasons leading to this result. On the one hand, the flexibility of the basal portion is not as good as that of the middle portion. On the other hand, the culm-wall of the basal portion is so thick that, in the phase of heating, it tends to generate a marked thermal gradient in radial direction which may lead to inadequate softening for bamboo interior. On the basis of the above analyses, it was found that the bamboo pieces with large diameter, thin culm-wall, regular geometric shape and good flexibility are beneficial to flattening.

Fig. 6 Abb. 6
figure 6

Crack degree of the three portions

Rissausprägung der drei Halmabschnitte

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In summary, the test results of bamboo stressed flattening process were satisfactory. A total of 78.7 % samples were flattened successfully which verified the correctness of the theory and the feasibility of this process.

5 Conclusion

Bamboo has increasingly been exploited in engineering designs, for economical reasons as well as its eco-efficiency and technical merits. In order to overcome the processing limitations of this material, a new forming technique of bamboo stressed flattening process was introduced in this paper. A device adapted to a manual laboratory hot-press was designed and constructed for the stressed flattening test of bamboo pieces. It was found that the middle portion samples showed the best flattening result, followed by the basal portion, while the top portion was the worst. Overall, nearly 80 % of the bamboo samples were flattened successfully and the final results of the test were satisfactory.