Analysis of the Relationship Between Microstructure and Elastic Properties of the Cell Wall

Authors

  • R. C. Tang
  • N. N. Hsu

Keywords:

Cell-wall model, composite material theory, elastic constants

Abstract

A three-dimensional analysis of the relationship between the microstructure and the anisotropic elastic properties of the cell wall was made, using the theory of composite materials. In particular, the influence of the orientation of microfibrils in each layer, crossed helical structure, thickness of layers, and the spacing between the rectangular reinforced microfibrils to such properties were explored; spacing between microfibrils in each wall layer was found to be critical, and presence of crossed helices in the Sa layer and the S2 micro-fibril angles was found significant in relation to elastic properties. Numerical data of all elastic constants of the cell wall were evaluated for five hypothetical models that included the fibers of earlywood, latewood, and compression wood. Theoretical data of the axial Young's modulus of the wood fibers were compared with those values obtained from static tension tests and sonic tests by other investigators. The inadequacy of the technique used in the static tension tests of wood fibers was discussed, and a proper approach for such analysis was suggested.

References

Barber, N. F. 1968. A theoretical model of shrinking wood. Holzforschung 22(4):97-103.nBarber, N. F., and B. A. Meylan. 1964. The anisotropic shrinkage of wood. Holzforschung 18(5):146-156.nBarrett, J. D., A. P. Schniewind, and R. L. Taylor. 1972. Theoretical shrinkage model for wood cell walls. Wood Sci. 4(3):178-192.nBoutelje, J. 1962. On shrinkage and change in microscopic void volume during drying, as calculated from measurements on microtome cross sections of Swedish pine (Pinus sylvestus L.). Sven. Papperstidn. 65(6): 209-215.nBritt, K. W., and P. N. Yiannos. 1964. The strength of paper-making fibers. Tappi 47(7):427-431.nCave, I. D. 1968. The anisntropic elasticity of the plane cell wall. Wood Sci. Technol. 2(4):268-278.nCave, I. D. 1969. The longitudinal Young's modulus of Pinus radiata.Wood Sci. Technol. 3(1):40-48.nChou, P. C., J. Carleone, and C. M. Hsu. 1972. Elastic constants of layered media. J. Compos. Mater. 6:80-93.nCockrell., R. A. 1946. Influence of fibril angle on longitudinal shrinkage of ponderosa pine wood. J. For. 44:876-878.nDinwoodie, J. M. 1965. Tensile strength of individual compression wood fibers and its influence on properties of paper. Nature 205:763-764.nDunning, C. E. 1968. Cell wall morphology of longleaf pine latewood. Wood Sci. 1(2):65-76.nEllwood, W. L., and W. W. Wilcox. 1962. Shrinkage of cell walls and cell cavities in wood microsections. For. Prod. J. 12:235-239.nFrei, E., R. D. Preston, and G. W. Ripley. 1957. The fine structure of the walls of conifer tracheids. VI. Electron microscope investigations of sections. J. Exp. Bot. 8:139-146.nFrey-Wyssling, A. 1954. The fine structure of cellulose microfibrils. Science 119:80-82.nGillis, P. P. 1970. Elastic moduli for plane stress analyses of unidirectional composites with anisotropic rectangular reinforcements. Fibre Sci. Technol. 2:193-210.nHarada, H. 1965. Ultrastructure and organization of gymnosperm cell walls. Pages 215-233 in W. A. Còté, Jr., ed. Cellular ultrastructure of woody plants. Syracuse Univ. Press.nHarris, M. J., and B. A. Meylan. 1965. The influence of microfibril angle on longitudinal and tangential shrinkage in Pinus radiata.Holzforschung 19(5):144-153.nHartler, N., C. Kull, and L. Stockman. 1963. Determination of fiber strength through measurement of individuaal fibers. Sven. Papperstidn. 66(8):301-308.nHodge, A. J., and A. B. Wardrop. 1950. An electron microscopic investigation of the cell wall organization of conifer tracheids and conifer cambium. Aust. J. Sci. Res. B3(3):265-269.nHosoi, II., K. Katahara, and N. Migita. 1958. Researches on the swelling of fibers. III relationship between the morphological structure and the behavior of swelling of fibers. J. Jap. Wood Res. Soc. 4(2):60-66.nJayne, B. A. 1959. Mechanical properties of wood fibers. Tappi 42 (6): 461-467.nJayne, B. A. 1960. Some mechanical properties of wood fibers in tension. For. Prod. J. 10(6):316-322.nJenzen, C. A. 1964. The effect of stress applied during drying on some of the properties of individual pulp fibers. Tappi 47(7):412-418.nKellogg, R. M., and F. F. Wangaard. 1964. Influence of fiber strength on sheet properties of hardwood pulp. Tappi 47(6) :361-367.nKelsey, K. E. 1963. A critical review of the relationship between the shrinkage and the structure of wood. CSIRO Div. For. Prod. Tech. Paper No. 28.nKollmann, F. 1951. Technologie des Holzes und der Holzwerkstoffe. Springer, Berlin. I, 327.nLeopold, B. 1966. Effect of pulp processing on individual fiber strength. Tappi 49(7):315-318.nLeopold, B., and D. C. McIntosh. 1961. Chemical composition and physical properties of wood fibers III. Tensile strength of individual fibers from alkali extracted loblolly pine holocellulose. Tappi 44(3):325-340.nMcIntosh, D. C. 1965. Wall structure of loblolly pine summerwood holocellulose fibers in relation to individual fiber strength. Pages 561-572 in W. A. Còté, Jr., ed. Cellular ultra-structure of woody plants. Syracuse Univ. PressnMark, R. E. 1967. Cell wall mechanics of tracheids. Yale Univ. Press.nMark, R. E., and P. P. Gillis. 1970. New models in cell-wall mechanics. Wood Fiber 2(2):79-95.nMark, R. E., P. N. Kaloni, R. C. Tang, and P. P. Gillis. 1969. Solid mechanics and crystal physics as tools for cellulose structure investigation. Text. Res. 39(3):203-212.nMeiser, II. 1955. Uber der Zellwandbau durch Holzvernorschung-spilze und die submikro-skopische Struktur von Fichtentraeiden und Birkenholzfasern. Holz Roh-Werkst. 13:323-338.nMeylan, B. A. 1968. On the cause of high longitudinal shrinkage in wood. For. Prod. J. 18(4):75-78.nNakato, K. 1958. On the cause of the anisotropic shrinkage and swelling of wood. IX. On the relationship between the microscopic structure and the anisotropic shrinkage in transverse section. J. Jap. Wood Res. Soc. 4(4):134-141.nPaul, B. 1960. Prediction of elastic constants of multi-phase materials. Trans. AIME 218:36-41.nPreston, R. D. 1965. Interdisciplinary approaches to wood structure. Pages 1-31 in W. A. Còté, Jr., ed. Cellular ultrastructure of woody plants. Syracuse Univ. Press.nSadoh, T., and G. N. Christensen. 1967. Longitudinal shrinkage of wood. Part I. Longitudinal shrinkage of thin sections. Wood Sci. Technol. 1:26-44.nSadoh, T., and R. S. T. Kingston. 1967. Longitudinal shrinkage of wood. Part II: The relation between shrinkage and structure. Wood Sci. Technol. I(2):81-98.nSamuelsson, L. G. 1964. Stiffness of pulp fibers. Sven. Papperstidn. 67:905-910.nSchniewind, A. P. 1970. Elastic behavior of the wood fiber. In B. A. Jayne, ed, Theory and design of wood and fiber composite materials. Univ. Washington, Seattle.nSchniewind, A. P., and J. D. Barrett. 1969. Cell-wall model with complete shear restraint. Wood Fiber 1(3):205-214.nStamm, A. J., and W. E. Smith. 1909. Laminar sorption and swelling theory for wood and cellulose. Wood Sci. Technol. 3(4) :301-323.nTang, R. C. 1972. Three-dimensional analysis of elastic behavior of wood fibers. Wood Fiber 3(4):210-219.nTang, R. C. 1973. The microfibrillar orientation in cell-wall layers of Virginia pine tracheids. Wood Sci. 5(3):181-186.nWardrop, A. B. 1951. Cell-wall organization and the properties of the xylem. I. Cell-wall organization and the variation of breaking load in tension of the xylem in conifer stems. Aust. J. Sci. Res. B4: 391-414.nWardrop, A. B. 1957. The organization and properties of the outer layer of the secondary wall in conifer tracheids. Holzforschung 11(4):102-110.nWardrop, A. B. 1964. The structure and formation of the cell wall in xylem. Pages 87-134 in M. H. Zimmermann, ed. The formation of wood in forest trees. Academic Press, New York.nYiannos, P. N., and D. L. Taylor. 1967. Dynamic modulus of thin wood sections. Tappi 50(1):40-47.nYlinen, A., and P. Jumppanen. 1967. Theory of the shrinkage of wood. Wood Sci. Technol. 1:241-252.n

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Published

2007-06-05

Issue

Number 2 / Summer 1973

Section

Research Contributions

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