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115 Cards in this Set

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What is the most common coordinate rotation?
The most common coordinate rotation is about the principle material axis 3 (z) thru an angle (theta)

*where theta is measured + in counter-clockwise direction from x axis to 1 axis
Why is shrinkage more opposed in the 1 direction?
Shrinkage is more opposed in the 1 direction because it's stronger in the 1 direction
What assumptions can be made when dealing with a tensile test for specimens where fibers are at an angle (theta) WRT longitudinal direction (ie: uniaxial stress, sigma_x)?
sigma_y = sigma_z
tao_yz = tao_xz = tao_xy = 0

Also, apply Hooke's Law:
sigma_x = E_x*epsilon_x
Name the 5 components of the cell wall
1.) cellulose
2.) elementary fibrils
3.) microfibrils
4.) hemicellulose
5.) lignin
Describe the cellulose component of the cell wall
*40-45% of dry wood
*linear polymer (ie: unbranched)
*beta (1-4) d-glucosepyranose units
*H-bonding is IMPORTANT; they hold the network flat

intra and inter molecular H-bonding

*sigma bonds and free rotation, but cellulose's H-bonds force it into ribbon-like structures and zip together to form crystalline structures
Describe the elementary fibrils of the cell wall
*composed of 50-80 cellulose units
*aligned as a parallel array w/a fibril axis
*the vertical 1 direction (up) pulls against covalent bonds and are aligned with cellulose chains

*the horizontal 2 direction (right) pulls against H-bonds
List some common numbers for elementary fibril parameters

ie: cross section and length
*elliptical or rectangular cross-section: 3.5 x 3.5 nm

*length: 0.1-40 microns
6 microns = 11,500 gluc, units
Describe the microfibrils of the cell wall
*have different directional arrangements in various layers of the cell wall

*in the S2 layer, arranged nearly VERTICAL

*mechanical properties = ANISOTROPIC

*however, recent studies suggest approx. transversely isotropic
List some common numbers for microfibril parameters

ie: E1, E2, G12, nu12

E1: 134 GPa
E2: 27 GPa
G12: 4.4 GPa
nu12: 0.1
1.) Fibrils are embedded in a matrix of ___ and ____.

2.) In the cell wall, microfibrils are bundled together into ____.
*1.) Fibrils are embedded in a matrix of HEMICELLULOSE and LIGNIN.

*2.) In the cell wall, microfibrils are bundled together into FIBRILS.
Describe the hemicellulose of the cell wall
*20-35% of dry wood

*BRANCHED heteropolymers

*it's an AMORPHOUS polymer

*Tg = 150-220 degrees C

*its mechanical props aren't totally understood
Describe the lignin of the cell wall
*20-30% of dry wood

*3D random polymer

*AMORPHOUS polymer

*Tg > 150 degrees C
List common mechanical properties of lignin

ie: E, G, poisson's ratio (nu)

E = 4 GPa

G = 1.5 GPa

nu = 0.5
Which layer of the cell wall occupies the largest portion?
S2 layer!

-most of the mechanical properties of the cell wall are determined by the S2 layer
How can we treat the cell wall as a continuous fiber composite?
Treat the cell wall as a continuous fiber composite:

cellulose microfibrils = reinforcing fibrils

lignin-hemicellulose = matrix
What is the fibril angle?
The fibril angle is the angle that cellulose microfibrils make with the fiber axis

fiber modulus = f(fibril angle)
What are some assumptions we can make about mechanical properties of the cell wall?
1.) the S2 layer of the cell wall is primarily responsible for mechanical properties of fiber

2.) fibril constant in a wood fiber

3.) The S2 layer has structure and symmetry similar to continuous fiber composite

4.) Fibers are processed, and the lumen collapses
Describe how the structure of fiber resemble a 2 layer laminate.
The fiber cross section is composed of an upper and lower ply, where each of their fibril angles are opposite
When you treat the material as an orthotropic lamina, do the collapsed walls interact?
No, the collapsed walls don't interect

-there is shear-shear coupling and shear-normal coupling

*see matrix!
Describe how the shear strain's tied to normal stress
In the shear-normal coupling, the load is transferred over to the fiber, and the fiber undergoes tensile forces...there's strain in the direction of the fiber

...ie: this is where the tao term comes from (from the coupling)
What is Zero Span Tensile Testing?
Zero Span Tensile Testing is a special type of test run on paper samples with clamps at zero separation (span)

-it's used to gage fiber STRENGTH

strength =
load to break/width of sample
How are strength and cellulose related?
As cellulose increases, the strength also increase
What is the breaking length?
breaking length =
length of strip necessary to break the sample under its own weight

Z ~ 4,000-15,000 meters
What is the relationship between the fibril angle, E, and TS?
as fibril angle (theta) increases...

E & TS along fiber axis decrease
What is the relationship between the mass fraction of cellulose, E, and TS?
as mass fraction of cellulose increases (up to 80%)

E & TS along fiber axis increase
What's the relationship between defects in the material, E, and TS?
as the concentration of defects (knicks, scratches) increases

E & TS along fiber axis decrease
What are the typical ranges for fiber properties?

ie: E, TS, sigma_y
Range for Fiber Properties:

E = 10-100 GPa

TS = 200-1800 MPa

sigma_y = 100 MPa
Relate the properties of fiber to the properties of paper

ie: E, TS, and sigma_y
Fiber properties (E, TS, and sigma_y) are far larger than Paper properties (E, TS, and sigma_y)
What is the crystalline phase?
The crystalline phase is where ions, atoms, or molecules exist as periodic (or 3D) arrays and repeating; ordered.
What is the amorphous phase?
The amorphous phase is characterized as disordered, and non-crystalline
Are crystalline polymers crystalline?
No! Crystalline polymers are not completely crystalline
What is the Fringed Micelle Model?
The Fringed Micelle Model is where cellulose is divided between
crystalline and amorphous regions

~(either highly ordered or highly disordered)
What are crystallites?
Crystallites are part of the Fringed Micelle Model, and are characterized as stiff and strong
What are physical properties of the amorphous regions in the Fringed Micelle Model?
Amorphous regions are part of the Fringed Micelle Model, and are characterized as glassy and viscoelastic
Describe an amorphous polymer
Amorphous polymers are viscoelastic (ie: viscous and elastic)...they're both fluid and solid-like

their mechanical properties = f (t, T)
What are the 5 regions of Fringed Micelle Model behavior?

*ie: think of the semi-log plot:
log(Young's Modulus) vs Temp
The 5 Regions of Behavior:

1.) Glassy Region
2.) Glass-Rubber/Glass Transition Region

3.) Rubbery Plateau Region

4.) Liquid Flow Region

5.) Rubbery Flow Region
What is the glassy region?
The glassy region is stiff and strong

E is constant
What is the glass-rubber/glass transition region?
The glass-rubber/glass transition region is where there's a drop of stiffness and strength of several orders of magnitude over ~10-20 degrees C
What is the rubbery-plateau region?
The rubbery-plateau region is where the mat'l is like a rubber band...as the temp increases, the density decreases

strength & stiffness = f(density)
What is the liq. flow region?
The liq. flow region is where the mat'l is melted
What is the rubbery flow region?
The rubbery flow region is where the mat'l is like taffy (for cross-linked systems!)
What is T_g?
T_g is the glass transition temp
What is T_m?
T_m is the melting point for the crystalline region
What are some standard glass transition temperatures for lignin and hemicellulose?
T_g: [degrees C]

lignin: > 150

hemicellulose: 150-220
What is the relation between T_g and moisture content?
As T_g decreases, the moisture content increases

= f(plasticizer)
*polymeric chains slide past each-other more easily
What % is LOW moisture content for wood fiber?
Low moisture content = < 18%
What % is HIGH moisture content for wood fiber?
High moisture content = > 18%
How does moisture move in wood fiber?
Moisture moves in AMORPHOUS REGIONS (more vol!) and this affects the ASPECT RATIO

aspect ratio = l/d
What's the relation between amorphous regions and the aspect ratio?
The soaking amorphous regions decrease the aspect ratio

*it breaks the fiber up into short fiber composites
What are typical values of a fiber LENGTH and WIDTH?

length = 0.5-5.0 mm

width = 10 - 50 microns
What is a typical value for fiber aspect ratio? (l/d)

aspect ratio = 50-100
What is a typical value for the cross-sectional perimeter of fiber, P_f?

cross-sectional perimeter = 92 microns
What is the typical value for the cell wall thickness of fiber, d_f?

cell wall thickness = 2.5-7 microns
What is the typical value for the cell wall density of fiber, rho_f?

cell wall density = 1.5 g/mL
What is the typical value for the cross-sectional area of fiber, A_f?

cross-sectional area = 100-500 microns^2
What is the typical value of the coarseness of fiber?

coarseness = 0.1-0.3 mg/m
What is the typical value of the basis wt of fiber, b_f?

basis wt = 3-10 g/m^2
What is the typical value of the wt. of fiber, wt_f?

wt = 1 microgram
Name two types of pulping methods
1.) Mechanical pulping

2.) Chemical pulping
Describe mechanical pulping methods
Mechanical pulping grinds down the material -- keeps it all, none is lost
Describe chemical pulping methods
Chemical pulping breaks up the lignin and dissolves it
-also dissolves hemicellulose
What are "fines"?
"Fines" are the portion of fiber solids that pass thru 200 mesh screen

(openings in mesh ~ 76 microns)
What is internal fibrillation?

or "delamination of the cell wall"?
Internal fibrillation:
-breaking fibrils apart from each other
-microfibrils broken free
-tearing holes in cell wall = more porous

more porous = more H2O uptake
What is a result of more H2O uptake as a result of internal fibrillation?
(ie: increased porosity)
More H2O uptake makes the fiber more supple and the cell wall softens

-the lumen collapses
-the fiber changes from rigid rod to flexible ribbon!
What is external fibrillation?

ie: "peeling of cell wall"
External fibrillation is thought of as "making the structure fuzzy"...
-peels the microfibrils in secondary cell wall

-the specific surface area increases (area/mass)

-there are a lot of "fines" (because of the peeling and breaking off)

-drainage decreases; it's diff. to get H2O out

-efficiency of wet-end chemicals goes down
What happens to the TS with external fibrillation?
External fibrillation increases the TS of paper because...

1.) better bonding!
2.) fills void mat'l and density increases
What is "wet web"?
Wet Web Strength is where fibers are held together by capillary forces
What is the relation between wet web and external fibrillation?
External fibrillation increases wet web strength
What are results of low consistency refining?

ie: low solids in H2O when refining
Low Consistency Refining:

defects concentration and breaking strength = decrease

elasticity & TS = increase

*straightens out defects!
*becomes more brittle!
What are results of high consistency refining?

ie: high conc. of solids in H2O
High Consistency Refining:

elasticity & TS = decrease

defect concentration = increase

*becomes more ductile!
What's important to know about shrinkage and drying direction?
The shrinkage perpendicular to the fiber axis is approx. 10 times the % of shrinkage parallel to the fiber axis

ie: fiber pulls back on itself because its weaker in the transverse direction
What is Jentzen's Observation?

1.) Drying never-dried-before fibers under an axial load causes elasticity and TS to increase and breaking strength to decrease..becomes more brittle

2.) There's no change in properties when experiments were run w/one-dried fibers

3.) Drying fibers under COMPRESSIVE LOAD causes:
TS = decrease
E = decrease
breaking strength = increase

therefore: becomes softer, weaker, and more ductile
What are TS, elasticity, breaking strength, and yield strength all functions of?
TS, E, breaking strength, and sigma_y = f(cellulose content, fibril angle, and concentration of defects)
What happens when you dry never-before-dried fibers under AN AXIAL LOAD?
Drying NBD'ed fibers under an AXIAL LOAD removes defects and straightens out the fibril angle
What happens when you dry never-before-dried fibers under a COMPRESSIVE LOAD?
Drying NBD'ed fibers under a COMPRESSIVE LOAD introduces defects and increases fibril angle
Why are never-before-dried fibers useful?
NBD'ed fibers prevent the irreversible change of cell-wall thickening

..otherwise wouldn't be able to change the fibril angle

ie: when fiber is dried = irreversible changes in cell wall!
Describe the capillary forces that create the "wet web" effect
-The capillary forces hold paper together after all the water is out of it

-The curved surface interface creates a pressure gradient that pushes & holds the fibers together
For machine-made paper, which direction contains the most oriented fibers?
More fibers are oriented in MD
What are the effects of the MD having more oriented fibers?
There's a difference between jet and wire speeds (v_s)...

v_s > 0 : rush conditions

v_s < 0 : drag conditions

v_s ^ = MD orientation ^

turbulence ^ = MD orientation v
How are fiber-fiber bonds and fiber shrinkage related?
Think of the overlapped bonded regions and unbonded free-segments..

the BONDED REGIONS have a % shrinkage in the transverse direction (perpendicular to fiber axis) GREATER than shrinkage parallel to fiber axis (longitudinal)

therefore: can ignore shrinkage parallel to fiber axis
What kind of forces are applied along fiber axis in bonded regions during drying?
During drying, the bonded regions experience compressive forces
What is unrestrained drying?
Unrestrained drying:

-the ends of the fibers aren't held
-there's significant fiber shrinkage (esp in bonded regions!)
-the free segments are left relatively unaffected
What is restrained drying?
Restrained drying:

-both ends of the fiber are held
-there's little fiber shrinkage
-there's expansion of the free segments (they get stretched~)

...sort of like drying the free segments under tensile load, because they get stiffer and stronger like Jentzen's Observation
Fibers in machine-made paper are stronger in the machine direction (MD) than the cross direction (CD) except for what parameter?
The result of restrained drying causes:

breaking strength in MD < breaking strength in CD
What is RBA?
Relative Bond Area, RBA, =
bonded surface area in a sheet of paper / total surface area of the sheet

*measures via {gas adsorption, light scattering, & density changes}
How are density and bulk related?
density =
basis wt / average sheet thickness

bulk =
1 / density
What is porosity?
porosity =
1 - (density of the sheet/ density of the cell wall)
Why is the sheet thickness (caliper) of paper hard to calculate?
The sheet thickness is ambiguous because the paper surface is so rough.

-therefore, we use the apparent thickness...place paper between circular plates and apply light pressure

d_app = distance between plates
How are the apparent density, basis weight, and apparent diameter related?
apparent density =
basis weight / d_app
How is apparent bulk related to apparent density?
apparent bulk = 1 /apparent density...

apparent bulk = d_app / basis weight
What is a layered sheet?
A layered sheet:
most of the fibers are in the MD-CD plane

-produce paper at low consistency
What is a felted sheet?
Felted sheet: more fibers are oriented out of the MD-CD plane

-produce paper at higher consistency
Describe some aspects of in-plane tensile properties of paper.
-paper is orthotropic
-the MD direction is strong, because it's dried in the MD direction

-for thin sheets/plys, the stresses induced out-of-plane tend to be small relative to in-plane stresses
What are the 3 main conditions to consider for plane stress?
Plane stress conditions:

-stress in MD
-stress in CD
-shear stress in the MD-CD
What does the In-Plane Engineering Stress-Strain Diagram look like? Where are the MD and CD curves relative to each other?
The In-Plane Engineering Stress-Strain Diagram has 2 curves:

1.) MD curve is stronger, more brittle

2.) CD curve (below) is weaker, more ductile

MD [E, TS, & yield strength] are greater than CD [E, TS, & yield strength)


The breaking strength is higher in the CD and lower in the MD
What are the 2 different views for determining in-plane elastic properties?

(ie: 2 views for the stiffness of paper)
Views for the Stiffness of Paper:

1.) E = measure of H bond stiffness
*fibers are held by H-bonds, and the paper pull = stretching H-bonds

2.) E = measure of fiber stiffness
*the fiber-fiber bonds are stiff, so essentially pulling deforms the fibers
*therefore, can model LE behavior based on deformation of fibers
What is 'strain energy density (U)'?
U =
work to stretch paper to strain / vol paper

U = 1/2E*(strain^2)
How is the 'strain energy density' calculated for fiber, U_f?
U_f =
work to stretch fiber (strain_f) / vol fiber

U_f = 1/2(E_f)*((strain_f)^2)
Assuming stiff fiber-fiber bonds, how can we relate the volumes of the fiber and sheet to the densities of the fiber and sheet, and the average strains?
U = v_f / v_sheet * U_f

= rho_sheet/rho_f * (1/2 (E_f * ((strain_f)^2))
How is the strain solved for (= f(density of sheet, density of fiber, k, and fiber strain) ?
Set the 'strain energy density' eqns equal to each other

1/2E(strain^2) = 1/2 (rho_sheet/rho_f)E_f*((strain_f)^2)

solve for E....

E = [rho_sheet/rho_f]*k*E_f
What is 'k'?

ie:....think strain energy density
'k' is the efficiency factor

k = 1/3 for random distributions

k = (average strain_f)^2 / strain^2
What's a typical value for E_MD?
E_MD = 5 GPa
What's a typical value for E_CD?
E_CD = 2 GPa
What's a typical value for nu_MD?
nu_MD = 0.5
What's a typical value for nu_CD?
nu_CD = 0.2
What's a typical value for G_(MD-CD)
G_(MD-CD) = ~ 1 GPa
What leads to fiber failure?
Fiber failure:

1.) the fiber could rupture

2.) the bonds between the fibers could rupture
Why is there more of a chance that fiber failure is a result of bonds between fibers?

*recall: (TS)_p = 1/4*(TS)_f
Fibers are stronger than paper, therefore there's more evidence that failure is function of bonds between the fibers

....broken fibers are observed at the rupture line
....(TS)_p tends to be proportional to fraction of rupture-line fibers broken
What is the tensile strength of paper a function of?

....Page eqn...
tensile strength of paper = f(fiber-fiber bond strength and fiber strength)
What is the Page eqn?
1/TS = (9/8Z) + (3w_f)/(l_f*RBA*tao_b)

variables defined:

TS = force/area

z = zero span tensile strength (force/area)

w_f = average fiber width

l_f = average fiber length

RBA = relative bonded area

tao_b = shear strength of fiber-fiber bonds (force/area)
When does BOND STRENGTH dominate?

...Page eqn....
BOND STRENGTH dominates when
lim TS (as tao_b --> 0)
= (l_f *RBA*tao_b)/(3w_f)
When does FIBER STRENGTH dominate?

...Page eqn....
FIBER STRENGTH dominates when lim TS (as z --> 0)
= 8/9z
What does zero-span tensile strength (z) influence?
drying under a tensile load means the fiber will be stiffer, stronger, and more brittle = f(z)

*think --> z ~ fiber strength
What are some factors that influence bonding effects?
bonding effects:

TS increases as RBA increases
TS increases as tao_b increases
What are the typical values for tensile strength (TS) of MD and CD?
TS_MD = 50-60 MPa

TS_CD = 20 MPa