Advanced Materials Research Vols. 393-395 (2012) pp 453-457
Online available since 2011/Nov/22 at www.scientific.net
© (2012) Trans Tech Publications, Switzerland
doi:10.4028/www.scientific.net/AMR.393-395.453
The Model Theory on Structural Mechanics of Cell Disruption Force in
the Preparing Process of Superfine Wood-flour With Cryptomeria
Fortunei
Dongxia Yang1,2, a, Yan Ma1,b and Chunmei Yang1,c
1
College of Mechanical and Electronic Engineering Northeast Forestry University,
Harbin,150040, China
2
Harbin University, Harbin,150040, China
a
[email protected], [email protected], c [email protected]
Keywords: Superfine wood-flour, Cell disruption, Structural mechanics, Truss.
Abstract. In the process of preparing superfine wood-flour with physical method, when the size of
wood-flour particle reaches to the corresponding level, a single wood cell will be destroyed. In the
process of analyzing micro-nano wood-flour’s cutting power, the process of cell disruption of the
wood cell needs to be computed. Based on the relevant theory of finite element and structural
mechanics, this article builds a structure mode of 12 lever hexagon truss model to simulate the
cellular structure. There are 6 levers outside to simulate the cell and 6 levers inside to simulate the
internal pressure. This establishes a single cell stress model to analyze its stress. It can be obtained
that when the size of the force acting on the node reaches the unit force, the minimum tensile stress of
the bar element is bigger than the macroscopic tensile strength of the wood. According to the
structural characteristics of the cell wall, this paper compares the tensile stress along the grain of the
bar element with the tradition cutting stress. Using tensile strength as the criteria to test the rupture
failure of Cryptomeria fortunei cell, the wood cell’s disruption force can be concluded. When
preparing superfine wood-flour with Cryptomeria fortunei as experimental raw materials, the
calculated results of applying the traditional cutting theory to calculate the cutting force has proved
the analysis structure of Cryptomeria cell micromechanics with the method of finite element and
structural mechanics, so that it can be concluded that certain cutting force can make Cryptomeria
fortunei cells disruption.
Introduction
When the wood is processed to several thousand nm, the wood is called ultrafine powders or
nano-particles. Now the granularity of the ultra-fine wood flour particle is defined between 1000 ~
20000 nm [1], but the general equivalent circle diameter wood cells is about 10 ~ 80µm, so when the
wood is processing to the ultra-fine wood flour particle size, the wood cell wall must be destroyed.
Therefore, the discussion of the broken force of the cell wall has important theoretical significance.
1. The establishment of the unicellular mechanical model
Plant cell consists of cell wall and cavity material, and the cell wall is a specific structure of the
plant cell. Wood cells are mainly composed of cellulose and hemi-cellulose ingredients. Cellulose
molecular chains give the mechanical strength to the wood and the hemi-cellulose can increase the
rigidity of the cell wall. The cell wall contains lignin which can enrich and rigid the cell wall [2].
The cell structure of the wood cross-section is similar to the hexagonal form observed by the
optical microscope, and the tracheid lumen which is on the inside of the regular cells can be
approximated to a circular cavity tube. According to the characteristics of wood cell structure and
though the structural principles of the three-dimensional simulation algorithm, the micron wood fiber
images can be transformed in three-dimensional coordinate according to the arrangement way of the
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cell tissue. Then the three-dimensional morphological modeling of the wood cells can be achieved on
the computer and the three-dimensional simulation diagram of the cell structure can be obtained
which is shown in Fig.1 [3]。 The length of wood cells is far greater than its sectional dimension, so
we got the establishment of the simplified mathematical model by the statistical analysis of the extra
cellular profile. After that we assume that the stress analysis of wood cells can meet the plane strain
state and the stress of wood cell characteristics can be discussed under the plane state.
Fig. 1 The cross section of wood rules cells and solid simulation of cell structure
The regular wood cells shown in Figure 1 will fall to pieces if it subject to greater cutting forces
and if it is processing to the micro-nano level, almost every cell must be broken in the crushing
process, so the research on cell-wall breaking is the basic research of wood crushing. In the processing
of the ultrafine wood powders the raw materials should be dried at first, because the wood fiber is
brittle in the low-water-content and which is in favor of the processing. The actual photo of the cells
crushing is in Fig. 2,
Fig. 2 The photos of cells were processed to cell disruption state
Wood is a natural non-homogeneous anisotropic polymer composite engineering material, and the
traditional research methods can not get the true mechanical properties of it. In this paper, the
structural model of wood cells was established by homogenization and the finite element method. For
the uniform and periodic microstructure shown in Figure 1, we can use a smallest unit cell as the
representative volume element and the strength of the wood cells are mainly in the cell wall.
Therefore, when the mechanical model of the wood cells was established, it was set in truss structure.
Two-dimensional hexagonal model of wood cell is composed of 12 linear elastic rods, 6 of them is
used to make the hexagonal simulation cell wall by rigid joint and the others are articulated into
star-like to simulate the internal pressure of the cell. As a mechanical model, this paper analyzed the
ideal state, for the triangular-shaped, quadrilateral, pentagon, etc. As long as one side is zero, that you
can get the ideal state. For non-regular hexagonal type, we just should change the length of rod.
Now for calculate the force of a single cell, we assumed that the model in Fig. 1 was subject to a
one-way compression force from top to bottom and take a cell unit i from it, the force of the unit can
be expressed in Fig. 3 by step. Fig. 3(1) shows the forces between cells and the vertical downward
compressive force of the cell unit i from two-dimensional tissue model can be replaced by node load
and node moment in the trusswork. Fig. 3(2) shows the supporting force of the cell unit under pressure
in the two-dimensional tissue model, and it can be expressed by axial force on node 4 and 5 along the
direction of the rods in the trusswork. Incorporate the force of Fig. 3(1) and 3(2), we got Fig. 3(3). Fig.
Advanced Materials Research Vols. 393-395
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3(4) shows the compressive force of the cell unit in the two-dimensional tissue model, and it can be
expressed by F on node 4 and 5. The force of the single-cell unit in Fig. 1 can be expressed by the
superimposed force in Fig. 3(4) and 3(3). Fig. 3 (3) and 3 (4) has become the standard force structure,
and the results can obtained in convenient by the finite element software.
Fig. 3 The forced model diagrams of a single cell
2. The broken force calculation in cell wall
During the analysis of the structural force in Fig. 3, the unit compressive stress of the rod unit (4)
was calculated by finite elements method in micro-mechanical. The core issue of the finite element
method was to derive the element stiffness matrix, and the displacement method was used in this
paper. Displacement values were calculated by using the formula {F} = [k] {∆}. When the force is
1kN, axial force diagram and deformation pattern in the two-dimensional model of cell organization
can be obtained by software simulation, shown in Fig. 4.On condition that the blade radius is close to
or greater than the average thickness of one pair cell wall, the fiber of the front cutting edge is pressed
bending not cited by the cutting edge at the cutting begin. Then the fiber in the front of the cutting
edge including below the cutting plane all generated tensile stress and the maximum value occurs
in minimum curvature radius of the cutting edge. When the tensile stress exceeds the ultimate tensile
strength of wood, the fiber in the front of the cutting edge pulled off and the cutting edge plays the role
in fiber cutting. With the increasing of the cutting force, the maximum force of the bar unit is the 6 bar
unit that imitate the intracellular pressure, the 4 bar unit at right and left sides which imitate the cell
wall take second place, and the minimum is the 2 bar unit at the top and bottom which imitate the cell
wall. This process happened to coincided with the destruction process of the wood cells after the
compression deformation under the effect of cutting force.
1. Axial force diagram
2. Deformed Shape
Fig.4 The axial force diagram and deformed shape diagram of cell tissue two-dimensional model
From the axial force diagram two-dimensional model of cell tissue we can see that different parts
of the rod unit are exposed to different axial force, and in the calculation we take the smallest axial
force of the upper and lower rod unit as the basis. Take the Japan cedar for example, tracheid
cross-section length of Japanese cedar is related to the earlywood and latewood. Here we take the
31µm as average value of the latewood[4]，when the pressure on node 4 and 5 in the cell model is
1kN, the minimum axial force of the rod is 0.07kN, and the tensile stress of the rod is 72.84MPa. The
tensile strength of the Anhui Xiuning cryptomeria in the fiber direction is 28.5MPa, and the tensile
stress of the rod is much greater than the macro tensile strength of wood. In the calculation of tensile
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Biotechnology, Chemical and Materials Engineering
stress of the rod unit in the cell model, the tracheid wall thickness affects the physical and mechanical
properties of wood, the thicker of the cell wall, the smaller the cell cavity is, the wood density is
larger, and the intensity is higher. Therefore, the tensile strength of the cell with thin and thick cell
wall can be simulated by structural mechanics. The critical value of axial force of the corresponding
rod unit was calculated between 5.14~9.34kN. It can be seen that so long as the cutting force applied
to the model is more than 9.34kN, the broken will occur in the rod unit of the cell model.
3. Make evidence for the cutting forces calculation of ultrafine powders in micromechanics by
the application of traditional cutting theory
The cutting of the ultrafine powders belongs to micro-nanometric cutting, and its stress analysis is
the scope of micro-mechanical, so the experimental verification of this result is almost impossible at
this stage. But it should be similar to the result go through with the traditional experimental
verification. During the cutting of raw materials, the cutting angle, cutting speed, species and the
cutting direction relative to the fiber direction all have an influence on the unit cutting force, reference
to the empirical formula of the cutting force[5]：
(1 − x)a h H
H − f 1'
(1)
] ( MPa) x =
H
eµ
In the equation, Kµis unit cutting force, µis friction coefficient between the cutter and material, eµis
the equivalent diameter of cellulosine, H is the relational functions between the main cutting force
and cellulosine, the coefficients A, B, C, H depend on tree species，cutting direction relative to the
fiber direction and the cutting method in vertical, horizontal or end grain cutting, aq, ah, x is the
modified coefficient in unit cutting force by the sharp blunt degree of the cutting edge.
When the ultrafine powders is being processed using the Japan cedar as the experimental materials,
take the cutter diameter D=280mm, the main shaft speed of the cutter n=7000r/min, the cutting angle
δ=5°. Through the calculation we got the unit cutting force Kµ=16.83MPa, and the cutting force of the
main direction F= 13.33kN, which is much larger than 9.34kN. In the wood cutting theory, the
traditional method of calculation is often in less accurate within the safe range, therefore, the value
calculate which is greater than the finite element analysis is normal. If this calculation model
considers the anisotropy, the gap between the two calculations will be even greater. According to this
calculation, when the cutting force in the main direction F= 9.34kN, the truss rod in cell model was
fractured and the cell wall is broken.
K µ = 9.807[10 xa h H + a q ( Aδ + Bv − C ) +
4. Conclusion
This paper analyzed a damage case in cell wall which was one of the most common models of the
wood cell structure. Wood cross-section of the cell mode is closely related to its species, age, early
wood or late wood, and growth characteristics of each season's. The structural model is also different,
rectangular, triangular, curved six prism, etc. In this paper, the cell-wall breaking in various shapes
cells were all analyzed.
Other structure models can also be analyzed and calculated in subsequent work to improve the
calculation accuracy. And it also can be analyzed as a thin-walled bar, which can make the calculation
of the broken cell wall more useful reference. After the comparison with the traditional method, the
results in this paper have a certain amount of accuracy and credibility.
Biography: Yang Chun-mei(1977-),female, Associate Professor in Northeast Forestry University,
Harbin 150040, P.R. China
Biography: MaYan(1955-),male, Professor in Northeast Forestry University, Harbin 150040, P.R.
China
Advanced Materials Research Vols. 393-395
457
Acknowledgements
This work was financially supported by the National Natural Science Foundation of China (30800869)
and the National Natural Science Foundation of China (31070500) and Natural Science Foundation of
Heilongjiang Province (C201018) and Central university basic research special fund operating
expenses (DL09BB14).
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Biotechnology, Chemical and Materials Engineering
10.4028/www.scientific.net/AMR.393-395
The Model Theory on Structural Mechanics of Cell Disruption Force in the Preparing Process of
Superfine Wood-Flour with Cryptomeria fortunei
10.4028/www.scientific.net/AMR.393-395.453