Effect of bending on radial distribution density, MFA and MOE of bent bamboo

Bent bamboo springback behavior

Changing of Rd_l/s and Rc_l under different relative humidity with time is shown in Fig. 3. Chord length and ratio of long diameter to short diameter changed within 2% after 47 days under 33% RH, 59% RH, 98% RH, which indicate that bent bamboo springs back little and has a high dimensional stability under low or high humidity conditions.

Containing large amounts of silicon compounds¹⁹, bamboo has a smooth and high hydrophobicity surface²⁰ which resulted in maintaining the bamboo bent stability. We found limited dimensional changes of Rd_l/s, Rc_l with time because of viscose deformation recovery under high humidity in the biomaterial bamboo²¹.

Radial distribution of density, MFA and MOE

Radial distribution of density, MFA and MOE on C, N and T of bending bamboo section are shown in Fig. 4. Results show that the distribution along radial of density, MOE and MFA is similar, which MOE increased from bamboo yellow layer (YL) to bamboo green layer (GL), while MFA is much higher in YL compared to GL for all three samples.

Density distribution along radial direction

Density distributions along radial direction from YL to GL for C, N and T sample in bending bamboo are showed in Fig. 5a. A similar tendency of increasing density from YL to GL can be found in all three samples, with the density distribution of the C sample lower than the N sample. Arithmetic mean density values for C, N and T samples are calculated as 720.38 kg/m³, 775.97 kg/m³ and 742.75 kg/m³ separately, indicating that the mean density of C and T samples decreased compared with N sample in bending bamboo. The mean density of compression and tension wood also differed from tension wood, which showed positive correlation between density and tension wood fibres percentage^22,23. Density generally correlate strongly with wood shrinkage²⁴. The decrease of density in compression and tension part was helpful in improving the dimensional stability of bent bamboo.

Strain would come with increasing stress when material experience any kind of external force. In some cases, stress is not large enough to produce obvious deformation, but it is difficult to precisely measure stress and strain inside wood, bamboo, or other materials. In general, when there is large stress, strain is visible and can be measured more accurately. Bending is a kind of obvious strain with the material experiencing bending load ultimately resulting in bending section deformation^25,26. Tube section would change from circular to elliptical after bending²⁷, which is a function of different degrees and forms of pore deformation. Following pore deformation, section density redistribute (Fig. 5a), which result in stress redistribution on the bending section of inner, middle and outer side²⁸.

MFA distribution along radial direction

MFA is defined as an inclination of microfibrils from the longitudinal axis, which play an important role in determining the final mechanical properties of bamboo²⁹ and wood³⁰. There are a lot of factors which may affect MFA in wood or bamboo, such as ages^29,31, species³², and locations in cross-Sect. ³¹. Although previous research has been carried out on MFA distribution along radial direction by picking some points on the cross section³¹, little research has been done to examine the continuous distribution of MFA along radial direction.

MFA distributions along radial direction at a 0.1 mm resolution for sample C, N and T are shown in Fig. 5b. The MFA were highest (38° ~ 48°) in about 0.2 ~ 0.5 mm near YL, followed by sharp decrease (10° ~ 4°) in distance of 0.5 ~ 1.8 mm from YL. A small increase was saw in the last 1 mm for C and N, except T. Arithmetic mean MFA values for C, N and T are calculated as 12.5°, 8.3° and 8.3° in the whole bamboo wall thickness. Although MFA showed nearly same arithmetic mean value in samples N and T, the value of the outer half bamboo wall near the green part experienced the greatest bearing strength³². The C, N and T near the GL were calculated as 11.0°, 7.5° and 5.0° with larger distance between the three MFA distribution.

MFA plays an important role in physical properties, such as bending strength, Young’s modulus²⁹, and is also an effective character to show bamboo internal stress changing. Previous studies have shown a decrease in MFA with an increase in tension stress³², and an increase in MFA with an increase in compression³³. This agrees with the result of this study that shows these changes mainly occurred in the half outer bamboo wall. A decrease in MFA is represented by better alignment of cellulose along axis direction, which resulted in higher tensile strength³⁴. Likewise, an increase in MFA is represented by an increase longitudinal compression, which resulted in better bendability³⁵. This changing tendency of the MFA in the outer half T and C wall indicate that bamboo has good bending stability.

MOE distribution along radial direction

Materials suffer interior stress when bending is carried out with external loading force. However, when the external force is removed, there would be a springback tendency for the bending material caused by the interior stress. This bending springback property can be altered by curvature radius^36,37, bending method³⁷, and the mechanical properties of the bending material^38,39. As one of the most important mechanical properties, MOE has a negative correlation with bending springback property for bending members^40,41.

Uneven MOE distribution for C, N and T parts along radial direction is shown in Fig. 5c. The MOE rises with increasing distance from YL to GL for these three samples. The changes in MOE is relatively small at first, followed by large changes in the middle and ultimately dropping again in the last 0.2 mm. MOE value differs in order of T > N > C, which arithmetic mean value calculated as 15.72 GPa, 13.58 GPa, and 10.14 GPa, respectively. Arithmetic mean values of T, N and C were 6.73 GPa, 6.13 GPa, and 4.22 GPa for the first half tube wall (near YL) while 24.44 GPa, 20.81 GPa and 15.90 GPa for the latter half (near GL). There is a larger difference on the latter half tube wall than the first half tube wall, while the latter half tube wall bears a higher stress than the first half tube wall during bending.

Our results show that bending has an effect on MOE of the bending section. The MOE value shifts for both tension and compression parts compared with neutral part (Fig. 5c), which is likely due to microstructural changes under bending stress. For example, fiber orientation and degree of crystalline orientation would increase during tension, while decrease during compression^34,42, which is similar to an increase and a decrease in MOE during the tension and compression phase, respectively^43,44. The springback in bamboo is caused by multiple factors: (1) uneven distribution of stress along cross section (there is a higher stress in the outside half tube wall than the inside)⁴¹; (2) the higher MOE in the outside tube wall than the inside; and (3) the higher MOE in the first half bamboo tube wall than the latter half. These characteristics might be helpful to reduce springback for the bending bamboo.

Correlation between position, density, MFA & MOE

Correlation between position, density, MFA & MOE of compression (Fig. 6), neutral (Fig. 7) and tension (Fig. 8) parts is figured out. It shows a high correlation between position and density (R² = 0.85514 for C, 0.75553 for N and 0.79239 for T), position and MOE (R² = 0.82656 for C, 0.85549 for N and 0.85815 for T), MOE and density (R² = 0.9202 for C, 0.84819 for N and 0.92819 for T). The high correlation between position and density, position and MOE is caused by the radial distribution of density (Fig. 5a). Density is an important determinant to the strength of bamboo or wood^18,45, which made it a high correlation with MOE.

MOE is one of the most important mechanical properties for bending applications, which is influenced by density⁴⁶, MFA^47,48. MFA and density can have different effect on MOE, and is a function of species type. For example, MFA and density jointly account for 96% of the longitudinal MOE variation in Eucalyptus delegatensis⁴⁹, while MFA and density, separately account for 87% and 81% of the variation, respectively⁵⁰. Analysis of the relationship between MFA and density have shown negative correlation (− 0.59) in Pinus taeda L.⁵¹. Likewise, MFA and MOE showed larger variation along radial direction (400 kg/m³ ~ 1400 kg/m³ for density, 5° ~ 48° for MFA and 2 GPa ~ 40 GPa for MOE (Figs. 6, 7 and 8) than wood, indicating that correlations between density, MFA and MOE for the C, N and T part in bending bamboo, might differ with wood.

We found a good line correlation between MOE and density as shown in Figs. 6n, 7n, 8n and 9a, With proportion of variance of R² = 0.9202, 0.84819 and 0.92819 for C, N and N part respectively(Figs. 6, 7, 8, 9). This proportion of variance is higher than R² = 0.54 in moso bamboo, where density and MOE were estimated using drilling resistance technique and static bending test; respectively⁵². Likewise, it show R² = 0.47 in white oak, where density and MOE were analyzed using SilviScan, and R² = 0.70 in E. delegatensis, where density and MOE were estimated using SilviScan and vibration testing, respectively⁴⁹. Slope of MOE to density is0.03202, 0.04097 and 0.04501 for compression, neutral and tension part; respectively, which indicates that MOE is more sensitive to density during tension than compression.

While we found a strong linear correlation between MOE and density, there was a negative correlation between MOE and MFA as shown in Fig. 9b. Our results show the R² = 0.42835 for tension part when the expdec1 function was used. However, the correlation was low to meaningless in neutral (R² = − 0.00937) and compression (R² = 0.04631) samples, which indicate that MOE is more sensitive to density in tension part compared to neutral and compression part.

We also found an “impact diminishing” point, where MOE does not reduce further beyond the certain point of MFA. The “impact diminishing” point appears to be 16° in three kinds of eucalyptus species (plantation-grown E. globulus, E. nitens and E. regnans)⁵⁰. In this study, the “impact diminishing” point of the bending bamboo varied as position of the section changed. The “impact diminishing” points were 17.2°, 16.8° and 13.8° for tension, neutral and compression part separately.

A previous study has shown negative correlation between MFA and density in ineucalyptus globulus (r = − 0.66) and Pinus taeda L. (r = − 0.59)⁵³. In this study, there was no obvious linear correlation between MFA and density as shown in Figs. 6j, 7j, 8j and 9c. With some specific high MFA value points when density is below 800 kg/m³, MFA approaches to be constant when density changed. After removing the “impact diminishing” and above points, the MFA algebra average value were 6.0°, 6.9° and 8.5° for tension, neutral and compression part, respectively. This shows that MFA declined under tension and rises under compression, which is consistent with MFA changing tendency in tension and compression compared to normal wood^54,55.