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115 Cards in this Set
- Front
- Back
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What is the most common coordinate rotation?
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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 |
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Why is shrinkage more opposed in the 1 direction?
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Shrinkage is more opposed in the 1 direction because it's stronger in the 1 direction
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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)?
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Assumptions:
sigma_y = sigma_z tao_yz = tao_xz = tao_xy = 0 Also, apply Hooke's Law: sigma_x = E_x*epsilon_x |
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Name the 5 components of the cell wall
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1.) cellulose
2.) elementary fibrils 3.) microfibrils 4.) hemicellulose 5.) lignin |
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Describe the cellulose component of the cell wall
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*40-45% of dry wood
*linear polymer (ie: unbranched) *beta (1-4) d-glucosepyranose units *H-bonding is IMPORTANT; they hold the network flat note: 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 |
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Describe the elementary fibrils of the cell wall
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*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 |
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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 ~average: 6 microns = 11,500 gluc, units |
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Describe the microfibrils of the cell wall
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*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 |
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List some common numbers for microfibril parameters
ie: E1, E2, G12, nu12 |
Microfibrils
E1: 134 GPa E2: 27 GPa G12: 4.4 GPa nu12: 0.1 |
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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. |
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Describe the hemicellulose of the cell wall
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*20-35% of dry wood
*BRANCHED heteropolymers *it's an AMORPHOUS polymer *Tg = 150-220 degrees C *its mechanical props aren't totally understood |
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Describe the lignin of the cell wall
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*20-30% of dry wood
*3D random polymer *AMORPHOUS polymer *Tg > 150 degrees C |
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List common mechanical properties of lignin
ie: E, G, poisson's ratio (nu) |
Lignin:
E = 4 GPa G = 1.5 GPa nu = 0.5 |
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Which layer of the cell wall occupies the largest portion?
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S2 layer!
-most of the mechanical properties of the cell wall are determined by the S2 layer |
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How can we treat the cell wall as a continuous fiber composite?
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Treat the cell wall as a continuous fiber composite:
cellulose microfibrils = reinforcing fibrils lignin-hemicellulose = matrix |
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What is the fibril angle?
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The fibril angle is the angle that cellulose microfibrils make with the fiber axis
fiber modulus = f(fibril angle) |
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What are some assumptions we can make about mechanical properties of the cell wall?
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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 |
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Describe how the structure of fiber resemble a 2 layer laminate.
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The fiber cross section is composed of an upper and lower ply, where each of their fibril angles are opposite
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When you treat the material as an orthotropic lamina, do the collapsed walls interact?
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No, the collapsed walls don't interect
-there is shear-shear coupling and shear-normal coupling *see matrix! |
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Describe how the shear strain's tied to normal stress
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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) |
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What is Zero Span Tensile Testing?
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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 |
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How are strength and cellulose related?
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As cellulose increases, the strength also increase
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What is the breaking length?
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breaking length =
length of strip necessary to break the sample under its own weight Z ~ 4,000-15,000 meters |
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What is the relationship between the fibril angle, E, and TS?
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as fibril angle (theta) increases...
E & TS along fiber axis decrease |
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What is the relationship between the mass fraction of cellulose, E, and TS?
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as mass fraction of cellulose increases (up to 80%)
E & TS along fiber axis increase |
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What's the relationship between defects in the material, E, and TS?
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as the concentration of defects (knicks, scratches) increases
E & TS along fiber axis decrease |
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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 |
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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)
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What is the crystalline phase?
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The crystalline phase is where ions, atoms, or molecules exist as periodic (or 3D) arrays and repeating; ordered.
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What is the amorphous phase?
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The amorphous phase is characterized as disordered, and non-crystalline
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Are crystalline polymers crystalline?
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No! Crystalline polymers are not completely crystalline
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What is the Fringed Micelle Model?
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The Fringed Micelle Model is where cellulose is divided between
crystalline and amorphous regions ~(either highly ordered or highly disordered) |
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What are crystallites?
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Crystallites are part of the Fringed Micelle Model, and are characterized as stiff and strong
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What are physical properties of the amorphous regions in the Fringed Micelle Model?
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Amorphous regions are part of the Fringed Micelle Model, and are characterized as glassy and viscoelastic
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Describe an amorphous polymer
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Amorphous polymers are viscoelastic (ie: viscous and elastic)...they're both fluid and solid-like
their mechanical properties = f (t, T) |
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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 |
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What is the glassy region?
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The glassy region is stiff and strong
E is constant |
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What is the glass-rubber/glass transition region?
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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
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What is the rubbery-plateau region?
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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) |
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What is the liq. flow region?
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The liq. flow region is where the mat'l is melted
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What is the rubbery flow region?
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The rubbery flow region is where the mat'l is like taffy (for cross-linked systems!)
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What is T_g?
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T_g is the glass transition temp
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What is T_m?
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T_m is the melting point for the crystalline region
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What are some standard glass transition temperatures for lignin and hemicellulose?
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T_g: [degrees C]
lignin: > 150 hemicellulose: 150-220 |
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What is the relation between T_g and moisture content?
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As T_g decreases, the moisture content increases
= f(plasticizer) *polymeric chains slide past each-other more easily |
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What % is LOW moisture content for wood fiber?
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Low moisture content = < 18%
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What % is HIGH moisture content for wood fiber?
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High moisture content = > 18%
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How does moisture move in wood fiber?
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Moisture moves in AMORPHOUS REGIONS (more vol!) and this affects the ASPECT RATIO
aspect ratio = l/d |
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What's the relation between amorphous regions and the aspect ratio?
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The soaking amorphous regions decrease the aspect ratio
*it breaks the fiber up into short fiber composites |
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What are typical values of a fiber LENGTH and WIDTH?
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Fiber:
length = 0.5-5.0 mm width = 10 - 50 microns |
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What is a typical value for fiber aspect ratio? (l/d)
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Fiber:
aspect ratio = 50-100 |
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What is a typical value for the cross-sectional perimeter of fiber, P_f?
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Fiber:
cross-sectional perimeter = 92 microns |
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What is the typical value for the cell wall thickness of fiber, d_f?
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Fiber:
cell wall thickness = 2.5-7 microns |
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What is the typical value for the cell wall density of fiber, rho_f?
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Fiber:
cell wall density = 1.5 g/mL |
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What is the typical value for the cross-sectional area of fiber, A_f?
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Fiber:
cross-sectional area = 100-500 microns^2 |
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What is the typical value of the coarseness of fiber?
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Fiber:
coarseness = 0.1-0.3 mg/m |
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What is the typical value of the basis wt of fiber, b_f?
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Fiber:
basis wt = 3-10 g/m^2 |
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What is the typical value of the wt. of fiber, wt_f?
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Fiber:
wt = 1 microgram |
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Name two types of pulping methods
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1.) Mechanical pulping
2.) Chemical pulping |
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Describe mechanical pulping methods
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Mechanical pulping grinds down the material -- keeps it all, none is lost
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Describe chemical pulping methods
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Chemical pulping breaks up the lignin and dissolves it
-also dissolves hemicellulose |
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What are "fines"?
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"Fines" are the portion of fiber solids that pass thru 200 mesh screen
(openings in mesh ~ 76 microns) |
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What is internal fibrillation?
or "delamination of the cell wall"? |
Internal fibrillation:
-breaking fibrils apart from each other -microfibrils broken free -creates MORE INTERNAL VOL -tearing holes in cell wall = more porous more porous = more H2O uptake |
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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! -INCREASED BONDING SURFACE AREA |
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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 |
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What happens to the TS with external fibrillation?
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External fibrillation increases the TS of paper because...
1.) better bonding! 2.) fills void mat'l and density increases |
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What is "wet web"?
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Wet Web Strength is where fibers are held together by capillary forces
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What is the relation between wet web and external fibrillation?
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External fibrillation increases wet web strength
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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! |
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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! |
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What's important to know about shrinkage and drying direction?
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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 |
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What is Jentzen's Observation?
....drying... |
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 |
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What are TS, elasticity, breaking strength, and yield strength all functions of?
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TS, E, breaking strength, and sigma_y = f(cellulose content, fibril angle, and concentration of defects)
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What happens when you dry never-before-dried fibers under AN AXIAL LOAD?
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Drying NBD'ed fibers under an AXIAL LOAD removes defects and straightens out the fibril angle
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What happens when you dry never-before-dried fibers under a COMPRESSIVE LOAD?
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Drying NBD'ed fibers under a COMPRESSIVE LOAD introduces defects and increases fibril angle
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Why are never-before-dried fibers useful?
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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! |
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Describe the capillary forces that create the "wet web" effect
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-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 |
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For machine-made paper, which direction contains the most oriented fibers?
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More fibers are oriented in MD
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What are the effects of the MD having more oriented fibers?
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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 |
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How are fiber-fiber bonds and fiber shrinkage related?
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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 |
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What kind of forces are applied along fiber axis in bonded regions during drying?
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During drying, the bonded regions experience compressive forces
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What is unrestrained drying?
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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 |
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What is restrained drying?
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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 |
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Fibers in machine-made paper are stronger in the machine direction (MD) than the cross direction (CD) except for what parameter?
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The result of restrained drying causes:
breaking strength in MD < breaking strength in CD |
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What is RBA?
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Relative Bond Area, RBA, =
bonded surface area in a sheet of paper / total surface area of the sheet *dimensionless *measures via {gas adsorption, light scattering, & density changes} |
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How are density and bulk related?
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density =
basis wt / average sheet thickness bulk = 1 / density |
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What is porosity?
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porosity =
1 - (density of the sheet/ density of the cell wall) |
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Why is the sheet thickness (caliper) of paper hard to calculate?
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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 |
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How are the apparent density, basis weight, and apparent diameter related?
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apparent density =
basis weight / d_app |
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How is apparent bulk related to apparent density?
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apparent bulk = 1 /apparent density...
apparent bulk = d_app / basis weight |
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What is a layered sheet?
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A layered sheet:
most of the fibers are in the MD-CD plane -produce paper at low consistency |
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What is a felted sheet?
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Felted sheet: more fibers are oriented out of the MD-CD plane
-produce paper at higher consistency |
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Describe some aspects of in-plane tensile properties of paper.
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-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 |
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What are the 3 main conditions to consider for plane stress?
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Plane stress conditions:
-stress in MD -stress in CD -shear stress in the MD-CD |
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What does the In-Plane Engineering Stress-Strain Diagram look like? Where are the MD and CD curves relative to each other?
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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) *but* The breaking strength is higher in the CD and lower in the MD |
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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 |
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What is 'strain energy density (U)'?
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U =
work to stretch paper to strain / vol paper U = 1/2E*(strain^2) |
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How is the 'strain energy density' calculated for fiber, U_f?
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U_f =
work to stretch fiber (strain_f) / vol fiber U_f = 1/2(E_f)*((strain_f)^2) |
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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?
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U = v_f / v_sheet * U_f
= rho_sheet/rho_f * (1/2 (E_f * ((strain_f)^2)) |
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How is the strain solved for (= f(density of sheet, density of fiber, k, and fiber strain) ?
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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 |
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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 |
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What's a typical value for E_MD?
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E_MD = 5 GPa
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What's a typical value for E_CD?
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E_CD = 2 GPa
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What's a typical value for nu_MD?
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nu_MD = 0.5
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What's a typical value for nu_CD?
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nu_CD = 0.2
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What's a typical value for G_(MD-CD)
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G_(MD-CD) = ~ 1 GPa
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What leads to fiber failure?
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Fiber failure:
1.) the fiber could rupture 2.) the bonds between the fibers could rupture |
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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 |
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What is the tensile strength of paper a function of?
....Page eqn... |
tensile strength of paper = f(fiber-fiber bond strength and fiber strength)
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What is the Page eqn?
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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) |
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When does BOND STRENGTH dominate?
...Page eqn.... |
BOND STRENGTH dominates when
lim TS (as tao_b --> 0) = (l_f *RBA*tao_b)/(3w_f) |
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When does FIBER STRENGTH dominate?
...Page eqn.... |
FIBER STRENGTH dominates when lim TS (as z --> 0)
= 8/9z |
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What does zero-span tensile strength (z) influence?
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drying under a tensile load means the fiber will be stiffer, stronger, and more brittle = f(z)
*think --> z ~ fiber strength |
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What are some factors that influence bonding effects?
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bonding effects:
TS increases as RBA increases TS increases as tao_b increases |
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What are the typical values for tensile strength (TS) of MD and CD?
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TS_MD = 50-60 MPa
TS_CD = 20 MPa |
