应压木细胞壁S_(2)层的微纤丝螺旋角对其抗压韧性的影响

Effects of microfibril helix angle in the S_(2)layer of compression wood cell wall on the compressive toughness of it

【目的】应压木细胞壁S_(2)层中的大微纤丝螺旋角(MFA)是树木管胞对力学环境适应性生长的结果,故它有其特别的力学性能。但目前人们还不了解S_(2)层中大MFA对其抗压性能的增韧机理。基于应压木细胞壁S_(2)层的超微结构建立复合材料力学模型,采用数值模拟方法研究应压木细胞壁S_(2)层中MFA对其抗压韧性的影响,可以探究其中的力学机理,并探索基于数值模型研究木细胞壁压缩韧性的建模与分析方法,进而为仿生材料设计奠定力学基础。【方法】首先将云杉木细胞壁S_(2)层简化为连续微纤丝和基体组成的复合材料,并利用夹杂理论的自洽模型计算木细胞壁S_(2)层基体的等效弹性常数。然后利用HyperWorks建立木细胞壁的纤维增强复合材料有限元分析模型,用Abaqus模拟不同MFA的应压木和正常木细胞壁S_(2)层在压缩载荷下的力学行为,并用所得结果分析其MFA与抗压韧性的关系。在此基础上,对比是否考虑木细胞壁的S_(1)、S_(3)(或S_(2)L,指的是S_(2)层与S_(1)层之间木质素和半纤维素含量高的区域)和MP层(P和ML层)对其受压力学行为的影响,并分析在应压木细胞壁数值模型中考虑各组分材料塑性行为的重要性。【结果】在压力作用下,当木细胞壁S_(2)层的MFA在0°~45°内增大时,其临界屈曲位移增大,临界屈曲压力先减小再增大。45°MFA应压木细胞壁S_(2)层的临界压力与0°MFA正常木细胞壁S_(2)层相当,但前者的临界屈曲位移是后者的3.57倍,屈曲失稳前的应变能是后者的2.95倍。在相同压力下,45°MFA应压木细胞壁S_(2)层微纤丝的von Mises应力低于0°MFA正常木。由于单个应压木细胞壁S_(2)层中螺旋状微纤丝所具有的压−扭耦合变形受到周边管胞对扭转变形的约束,其抗压刚度和抗压韧性得到增强。应压木细胞壁中的S 1、S_(2)L和MP层对其受压屈曲有显著的约束作用,完整应压木细胞壁的临界压力比只考虑S_(2)层的临界压力增大37.6%。压力作用下木细胞壁的破坏模式为塑性屈曲,所以考虑木细胞壁各组分材料的塑性行为对准确地计算其抗压韧性十分重要,忽略其塑性行为会使其临界压力的计算结果增大2.97倍。【结论】在受压状态下,应压木细胞壁S_(2)层中微纤丝的螺旋形貌改变了微纤丝与基体间的应力传递,使得S_(2)层的基体承受更多的压应力,木细胞壁的破坏模式变为局部塑性屈曲。所以在压力作用下,尽管应压木细胞壁的抗压刚度随S_(2)层MFA的增大而减小,但应压木细胞壁的临界屈曲位移随MFA的增大而显著地增大,从而增强了它的抗压韧性。当MFA为45°左右时,应压木细胞壁的抗压韧性最佳,此时不仅它的临界屈曲位移比正常木细胞壁S_(2)层高两倍多,且它的临界屈曲压力也略高于后者。

[Objective]The large microfibril helix angle(MFA)in the S_(2)layer of the compression wood cell wall is the result of the adaptive growth of tree tracheids to the mechanical stimulation,so it has special mechanical functions.However,the toughening mechanism of large MFA in S_(2)layer on the compressive properties of wood cell wall has not been understood yet by researchers.Based on a computational model of composite material for the ultrastructure of S_(2)layer of the compression wood cell wall,the effects of MFA in S_(2)layer on the compressive toughness of compression wood cell wall were simulated and the toughening mechanism was explored,and the method of modeling and analyzing the compressive toughness of the wood cell wall based on the numerical model was explored.The findings presented in this paper would provide useful guideline for the optimal design of biomimetic materials.[Method]First,the S_(2)layer of spruce wood cell wall was modeled as a composite cylinder composed of continuous microfibrils as well as matrix,and the equivalent elastic constants of the matrix of S_(2)layer were calculated using the self-consistent model of inclusion theory.Then,the finite element analysis model of the fiber reinforced composite of wood cell wall was established by HyperWorks.The compressive mechanical behaviors of the S_(2)layers of compression wood and normal wood with different MFA were simulated by Abaqus,and the relationship between MFA and the compressive toughness of S_(2)layer was analyzed.On this basis,the compressive mechanical behaviors of wood cell wall with and without S_(1),S_(3)(or S_(2)L,it means the area between S_(2)and S_(1) layer with high lignin and hemicellulose content)and MP(P and ML)layers were investigated,and the importance of considering the plastic behavior of each constituent in the numerical model of compression wood cell wall was analyzed.[Result]As the increasing of MFA(0°~45°)in S_(2)layer,the critical buckling displacement of S_(2)layer of wood cell wall was increasing,and the critical buckling pressure was first decreasing and then increasing.The critical pressure of S_(2)layer of compression wood cell wall with MFA of 45°was equivalent to that of normal wood cell wall with MFA=0°,but the critical buckling displacement of the former was 3.57 times of the latter,and the strain energy before buckling was 2.95 times of the latter.Under the same pressure,the von Mises stress of microfibrils in the compression wood S_(2)layer with MFA=45°was lower than that in the normal wood S_(2)layer with MFA=0°.The compressive stiffness and compressive toughness of S_(2)layer with large MFA were enhanced because the compression-torsion coupling of spiral microfibrils in S_(2)layer of a single compression wood cell wall was constrained by its surrounding tracheids.S1,S_(2)L and MP layers had significant restraint effect on the buckling of the compression wood cell wall,and the critical pressure of the compression wood cell wall with the consideration of all the layers in the wood cell wall was 37.6%larger than that of the model only considering the S_(2)layer.The failure mode of wood cell wall under pressure was of plastic buckling,so it is very important to include the plastic behavior of each component of wood cell wall to accurately calculate its compressive toughness.Ignoring the plastic behavior of wood cell wall will cause the computed result of its critical pressure increased by 2.97 times.[Conclusion]The spiral morphology of microfibrils in the S_(2)layer of compression wood cell wall changes the stress transfer between the microfibrils and the matrix,which results in the matrix of the S_(2)layer bearing more compressive stress and the failure mode of the wood cell wall becoming local plastic buckling.Although the compressive stiffness of compression wood cell wall decreases with the increase of MFA in S_(2)layer,the critical buckling displacement of cell wall increases significantly with the increase of MFA,thereby the compressive toughness of S_(2)layer is enhanced.When MFA is about 45°,the compressive toughness of S_(2)layer of compression wood cell wall reaches the highest,not only its critical buckling displacement is more than twice that of S_(2)layer of normal wood cell wall,but also its critical buckling pressure is slightly higher than the latter.