Density and Modulus of Elasticity (MOE) Distribution and Grading of Flattened Bamboo Boards

Abstract

The standardization of physical and mechanical properties is critical for the large-scale application of engineered bamboo products. In this study, the distribution characteristics of density and modulus of elasticity (MOE) were systematically examined in a large sample of flattened bamboo boards. The density and MOE ranged from 0.46 to 1.12 g/cm³ and 5.60 to 22.18 GPa, respectively. Both exhibited a decreasing trend with increasing board thickness. Based on interquartile analysis, four density grades and five MOE grades were established. A strong positive correlation was identified between density and MOE, indicating that density—closely linked to fiber volume fraction—is the primary factor influencing mechanical performance. Notably, the graded bamboo boards demonstrated significantly higher modulus values than conventional wood veneers such as hemlock and poplar, highlighting their potential for high-performance structural applications. This study proposes a practical grading framework that contributes to the standardization and broader engineering utilization of flattened bamboo boards.

1. Introduction

Bamboo is a natural, renewable, fast-growth, fiber-reinforced composite material with remarkable mechanical properties [1]. Various engineered bamboo products—including bamboo plywood, bamboo laminated lumber, and bamboo scrimber—have been largely utilized in furniture, construction, transportation, decoration, flooring, etc. [2,3,4]. In terms of chemical composition, bamboo is mainly composed of cellulose, hemicellulose, and lignin [5]. Hemicellulose is rich in hydrophilic groups such as free hydroxyl groups, which makes it highly hygroscopic and results in poor dimensional stability of bamboo. Heat treatment can significantly improve the dimensional stability of bamboo, but it will also affect the mechanical properties of bamboo [6]. At the micro scale, bamboo is a typical bio-composite which is composed of fibers as the strengthening units embedded in matrix-parenchyma cells [7,8]. The tensile strength of the fibers was approximately 11 times that of the matrix phase [9,10,11]. Consequently, the fiber content plays a critical role in the physical and mechanical properties of bamboo [12,13].

Bamboo and wood are both natural, renewable materials and represent the most fundamental raw materials used in construction. Currently, grading methods of wood lumber are being systematically developed and supported by a robust and comprehensive set of standards. Two primary approaches have been used for wood grading: visual grading and mechanical grading. Visual grading relies on identifying growth defects (such as knots and grain deviation) and processing defects (such as blunt edges, cracks, and warping) [14,15]. In contrast, mechanical grading determines the modulus of elasticity of dimensional lumber through standardized mechanical testing using specialized equipment, offering higher accuracy and efficiency [16].

Compared with wood, the grading systems for bamboo remain relatively underdeveloped. Although ISO 19624 outlines the fundamental principles and procedures for both visual and mechanical grading of round bamboo culms, it did not establish specific grading levels [17]. The diameter and linear mass ratio of bamboo culms serve as effective indicators for predicting their bending load-bearing capacity [18]. Additionally, the hardness modulus of the longitudinal end surface of bamboo culms was used to classify bamboo culm into six grades [19]. Moreover, there was a strong correlation between the mechanical properties of flattened bamboo boards and the hardness modulus of the original culms, suggesting that culm-based grading would predict board properties [20,21]. Dimension bamboo strips, the unit to bamboo laminated lumber, were divided into nine density grades and eight modulus grades to produce laminated lumber [22,23]. Acoustic wave velocity (V) was used to grade the MOE of notched flattened boards, achieving a high prediction accuracy (R² = 0.86) when combining density and velocity [24].

To standardize the properties of flattened bamboo boards, density and modulus of elasticity (MOE) distributions were evaluated and analyzed. The correlation between density and MOE, as well as the influencing factors, were systematically investigated. The results would provide a theoretical foundation for standardized classification, automated mechanical grading, and the rational engineering design of flattened bamboo boards.

2. Materials and Methods

2.1. Materials

Four-year-old Moso bamboo (Phyllostachys edulis (Carrière) J. Houzeau) culms harvested from Wuqiao Town, Gao’an City, Jiangxi Province, were processed into flattened bamboo boards through a series of process, including softening, non-notched flattening, shaping, and drying [25]. The resulting boards measured 1050–1100 mm in length and 90–100 mm in width. Three thickness categories were prepared: 2.1 mm (1000 pieces), 4.4 mm (1000 pieces), and 6.5 mm (730 pieces). The thickness of the bamboo culm wall gradually decreases from the base to the top, considering that in actual enterprise production, bamboo culms of different heights are used to manufacture flattened bamboo boards of different thicknesses. In order to more realistically reflect the actual production situation and provide more accurate guidance for the graded application of flattened bamboo boards, materials were sourced from the base towards the top to produce bamboo flattened boards with thicknesses of 6.5 mm, 4.4 mm, and 2.1 mm, respectively. All specimens were conditioned to a moisture content of 10% after drying.

2.2. Methods

The density of the flattened bamboo boards was measured according to the standard GB/T 19367-2022 [26]. The modulus of elasticity (MOE) was evaluated following the AITC T116 standard using a universal testing machine (Model 5582, Instron Corporation, Norwood, MA, USA) equipped with a 100 kN load cell [27]. The testing setup is shown in Figure 1. Loading was applied at the midpoint of the middle internode of each board, with a span-to-thickness ratio of 100:1. All specimens were tested with t with the denser vascular bundle side facing downward. The loading speed was determined based on the requirement that the elastic modulus test be completed within 30 s. The modulus of elasticity was calculated using the linear portion of the load–displacement curve, specifically within the 20%–40% load range of the proportional limit. Each specimen was tested six times, and the average of the last three measurements was the MOE value. The MOE was calculated using the following formula:

$$E={\displaystyle \frac{P{l}_2^3}{4\mathit{\Delta }b{d}^3}}$$

(1)

where E is the modulus of elasticity (MPa), P is the load difference (N), l₂ is the span between support rollers (mm), Δ is the deflection corresponding to P (mm), b is the width of the specimen (mm), and d is the thickness of the specimen (mm).

2.3. Statistical Analyses

Use the statistical software OriginPro 2022 (OriginLab Corp., Northampton, MA, USA) to conduct statistics on the density and MOE of the flattened bamboo boards, in order to analyze the performance differences in flattened bamboo boards with different thicknesses. The significance level in the analysis of variance is 1%.

3. Results

3.1. Variability and Distribution of Density and MOE in Flattened Bamboo Boards

The density and MOE of the flattened bamboo boards presented considerable variability. As shown in Table 1, the density ranged from 0.46 g/cm³ to 1.12 g/cm³, with an average of 0.76 g/cm³. The overall density distribution followed a normal distribution (Figure 2a). The MOE ranged from 5.60 GPa to 22.18 GPa, with an average value of 11.28 GPa, and its distribution was better represented by a log-normal model (Figure 2b).

As illustrated in Figure 2c,d, both the distribution range and the average values of density and MOE increased as the thickness decreased. The average densities for boards with thicknesses of 2.1 mm, 4.4 mm, and 6.5 mm were 0.80 g/cm³, 0.76 g/cm³, and 0.70 g/cm³, respectively. The corresponding minimum density values were 0.57 g/cm³, 0.49 g/cm³, and 0.48 g/cm³. Similarly, the average MOEs were 13.35 GPa, 10.59 GPa, and 9.32 GPa, respectively, with the maximum values reaching 22.18 GPa, 20.47 GPa, and 13.28 GPa (Table 1). Notably, the 2.1 mm thick boards exhibited significantly higher standard deviation (SD) and coefficient of variation (CV) in MOE compared to the thicker boards, indicating higher variability in their mechanical properties.

The special manufacturing process and the intrinsic gradient in fiber content of bamboo are critical factors influencing the density and modulus of flattened bamboo boards. During flattening, planning typically begins from the side with lower fiber content. As a result, higher planning leads to thinner boards and a higher proportion of retained high-fiber material (Figure 3). As shown in Figure 3, for flattened bamboo boards with target thicknesses of 2.1 mm, 4.4 mm, and 6.5 mm—produced from bamboo culms of identical wall thickness—the amount of material removed follows the order: 2.1 mm > 4.4 mm > 6.5 mm (Figure 3). Correspondingly, the retained fiber volume fraction decreases from 46.80% to 16.92% [28].

Table 1. Density and MOE span of flattened bamboo boards.

Units		Thicknesses (mm)	Density				MOE
			Density Range (g/cm3)	Average (g/cm3)	SD (g/cm3)	CV (%)	MOE Range (GPa)	Average (GPa)	SD (GPa)	CV (%)
Flattened bamboo boards		2.1	0.55–1.12	0.80	0.07	8.66	5.94–22.18	13.35	2.54	19.07
		4.4	0.61–1.10	0.76	0.07	9.71	7.09–20.47	10.59	1.56	14.76
		6.5	0.46–0.94	0.70	0.08	11.78	5.60–13.28	9.32	1.39	14.91
		Total	0.46–1.12	0.76	0.08	10.97	5.60–22.18	11.28	2.56	22.74
Dimension bamboo strips [29]		6.0	0.51–0.81	0.71	0.08	10.04	4.86–15.06	10.81	1.74	16.08
Bamboo properties at different heights [30]	1–3 m	9.7	0.71	-	-	-	6.52	-	-	-
	3–5 m	8.4	0.76	-	-	-	7.67	-	-	-
	5–7 m	7.1	0.77	-	-	-	9.86	-	-	-

Table 1. Density and MOE span of flattened bamboo boards.

Units		Thicknesses (mm)	Density				MOE
			Density Range (g/cm3)	Average (g/cm3)	SD (g/cm3)	CV (%)	MOE Range (GPa)	Average (GPa)	SD (GPa)	CV (%)
Flattened bamboo boards		2.1	0.55–1.12	0.80	0.07	8.66	5.94–22.18	13.35	2.54	19.07
		4.4	0.61–1.10	0.76	0.07	9.71	7.09–20.47	10.59	1.56	14.76
		6.5	0.46–0.94	0.70	0.08	11.78	5.60–13.28	9.32	1.39	14.91
		Total	0.46–1.12	0.76	0.08	10.97	5.60–22.18	11.28	2.56	22.74
Dimension bamboo strips [29]		6.0	0.51–0.81	0.71	0.08	10.04	4.86–15.06	10.81	1.74	16.08
Bamboo properties at different heights [30]	1–3 m	9.7	0.71	-	-	-	6.52	-	-	-
	3–5 m	8.4	0.76	-	-	-	7.67	-	-	-
	5–7 m	7.1	0.77	-	-	-	9.86	-	-	-

Compared with bamboo strips of similar thickness (Table 1), the average density of the 6.5 mm flattened bamboo boards was comparable to that of the bamboo strips, but the density distribution of the flattened boards is notably broader. In contrast, both the modulus range and the average modulus of the flattened boards are lower than those of the bamboo strips. This difference could be attributed, in part, to the thermal softening process conducted in saturated steam at temperatures over 160 °C, which resulted in a degradation of the bamboo’s mechanical properties [31].

In addition, the variation in wall thickness and mechanical properties along the height of bamboo culms also influences the density and modulus of flattened bamboo boards. To maximize material utilization, thinner boards were typically produced from the top sections of the culm with thinner culm wall. In this study, the three types of flattened bamboo boards were prepared from the base, middle, and top part of culms, respectively (Figure 3). As reported in previous studies [32], both density and fiber content increase from the base to the top of the culm, which corresponds to the observed trends in the flattened boards. Notably, at any given height, the mechanical performance of the flattened bamboo boards exceeded that of the original bamboo culm. This improvement could be attributed not only to variations in planning but also to the densification effect caused by radial compression during the flattening process [33,34].

3.2. Grading on Density and Modulus of Elasticity of Flattened Bamboo Boards

Based on the density and modulus distributions of a large sample of flattened bamboo boards, as well as the application requirements for bamboo-based materials, the boards were classified into four density levels (D1–D4) and five modulus levels (E1–E5), arranged from high to low. Classification was performed using the interquartile range method, considering the 25th to 75th percentiles for both density and modulus. The classification thresholds and their proportions are summarized in

Table 2. Density grades and MOE grades of flattened bamboo boards.

Grades	Range (g/cm3 or GPa)	Proportion (%)	Proportion of Different Thickness (%)			Hem-Fir Veneer [35]	Populus Tremuloides Veneer [36]
			2.1 mm	4.4 mm	6.5 mm
D1	>0.85	10.9	16.7	11.2	2.6	-	-
D2	(0.75, 0.85]	41.9	58	36.4	27.3	-	-
D3	(0.65, 0.75]	38.2	24.2	49.3	42.2	-	-
D4	≤0.65	9.0	1.1	3.1	27.9	-	-
E1	>18	1.8	4.5	0.3	0	15.17 (1.57 1)	13.24 (1.03 1)
E2	(15, 18]	8.1	20.7	1.2	0	11.86 (0.76 1)	12.14 (0.90 1)
E3	(12, 15]	22.4	43.4	15.4	2.4	9.17 (0.97 1)	10.35 (1.10 1)
E4	(9, 12]	51.4	28.2	70.4	58.0	-	-
E5	≤9	16.3	3.2	12.7	39.6	-	-
MOE variance analysis of flattened bamboo boards
Source of variation	SS	df	MS	F	p-value	F crit	Significance
Intergroup	8562.74	3	2854.25	871.85	0	3.79	*** 2
Within group	8456.20	2583	3.27
Total	17,018.94	2586
Density variance analysis of flattened bamboo boards
Source of variation	SS	Df	MS	F	p-value	F crit	Significance
Intergroup	7.13	4	1.78	746.74	0	3.33	*** 2
Within group	6.17	2582	0.0024
Total	13.30	2586

¹ The value in parentheses is the standard deviation.² *** Indicates that the significance is highly significant.

.

The majority of flattened bamboo boards were in density grades D2 (0.65–0.75 g/cm³) and D3 (0.75–0.85 g/cm³), accounting for 41.9% and 38.2%, respectively. These two grades constitute 80.1% of the total, which aligns well with the density distribution shown in Figure 2. In comparison, boards with densities less than or equal to 0.65 g/cm³ (D1) and higher than 0.85 g/cm³ (D4) represent 10.9% and 9.0%, respectively.

Regarding modulus classification, most boards fall into grades E3, E4, and E5, collectively comprising 90.1% of the samples. Grade E4 is the most prevalent, accounting for 51.4%. These results correspond with Figure 2, which indicates that the primary bending modulus range is between 8 and 15 GPa. Grades E1 and E2 constitute smaller fractions, at 1.8% and 8.1%, respectively.

Notably, within the same modulus grade, flattened bamboo boards exhibit significantly higher modulus values compared to common softwood and hardwood veneers such as hemlock and poplar. This indicates that flattened bamboo boards of corresponding modulus grades are well-suited for producing engineered panels with mechanical properties equal to or surpassing those of wood-based laminated products [37,38].

3.3. Correlation Between Density and MOE in Flattened Bamboo Boards

The relationship between the density and MOE in flattened bamboo boards was presented in Figure 4. MOE increased with the density increase. There was a nonlinear curve relationship between density and MOE, which fit a quadratic function: y = 29.94x² − 18.5x + 7.9, R² = 0.571. At 0.75 g/cm³ density, the MOE of flattened bamboo boards in different thicknesses was similar.

As shown in Figure 5a, the average moduli for panels with three thicknesses at this density are 11.28 GPa, 10.47 GPa, and 10.14 GPa, respectively, indicating only minor differences in modulus at equal density. Meanwhile, at the 10 GPa MOE level, Figure 5b showed that the average densities of flattened bamboo boards in different thicknesses were 0.73 g/cm³, 0.75 g/cm³, and 0.74 g/cm³, respectively. The small differences in density at the same flexural modulus suggest that the MOE of flattened bamboo boards was primarily determined by density, independent of thickness [39].

4. Conclusions

Based on the intrinsic gradient characteristics of bamboo and its unique flattening process, this study investigated a large sample of flattened bamboo boards to determine the distribution and ranges of their density and modulus. A classification method and grading system for flattened bamboo boards were proposed and established first. A significant positive correlation was found between density and modulus, with both properties decreasing as board thickness increases. At a certain grade level, the modulus of flattened bamboo boards was consistently higher than that of common softwood and hardwood veneers such as hemlock and poplar, highlighting their potential for use in high-performance structural plywood and laminated products. This study provided a standardized grading framework for flattened bamboo boards, offering important guidance for their practical application in structural and engineered panel products, and contributing to the broader utilization of bamboo in construction and engineering materials.