FiberMatrix Interface

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Fiber-Matrix Interface
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Fiber Matrix Interface

• Why are fiber matrix interfaces important?
• Ef Em quite differentSuch large differences
  are shared through the interface.Stresses acting
  on the matrix are transmitted to the fiber across
  the interface.
• The interfacial bond can influence
• Composite strength
• Modes of failure
• Youngs modulus
• Interlaminar shear strength
• Compressive strength
• Critical fiver length
• Environmental resistance
• Structural stability at elevate temperatures
• Fracture and fatigue behavior
• Weak interface Composites provide low strength
  and stiffness. Promotes fiber debonding and
  pull-out which provide higher fracture toughness
• Strong Interface Provides high strength but low
  fracture toughness (Except Short Fiber requires
  strong bonding for higher fracture toughness)

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Definition of Fiber-matrix Interface and
Interphase

• Interface It is the boundary demarcating the
  distinct phase of fiber, matrix and coating layer
• Interphase It is a region where coating and
  matrix diffused into each others domain and form
  a flexible, three-dimensional polymer network.
  The key purpose of the network is to provide a
  lattice that the matrix molecule can penetrate
  and come in close proximity to fibers. The
  interphase is responsible for transferring the
  load from the matrix to the fibers. Formation of
  interphase region and the resulting properties
  are poorly understood.
• Coating
• Sizing protect fibers from mechanical damage
• Finishes Enhance bonding of fiber to matrix
  (Polyvinyle acetate or organosilane coupling
  agent)
• Interphase probably has lower modulus and
  strength than fiber and matrix.

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Atomic Bonding

• Molecules Groupings of coordinated atoms
• Intramolecular bonds Bonds between atoms of a
  molecule (strong primary bonds i.e. covalent
  bond)
• Intermolecular bonds Bonds between the
  molecules (weak secondary bonds i.e. Van der
  Walls Bonds)Atoms are bonded in solid through
  exchange of electrons in outer shell (s,p
  level)i.e. covalent bond
• Valence Electron Electrons that participate in
  bonding or chamical reaction (s,p level
  electrons)
• Covalent Bond Bond in which atoms share two or
  more electrons (very strong primary bond)

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Van der Waals Bonding (secondary bonds)

• Join molecules or groups of atoms by weak
  electrostatic attractions. Many ceramics,
  plascits, and other molecules are permanently
  polarized such that regions of the molecule are
  positively (and negatively) charged.
• Electrostatic attractions between oppositely
  charged regions result in weak Van der Waals
  bonding between two molecules.
• H2O The electrons in the oxygen atoms tend to
  concentrate away from the hydrogen. The polarity
  of the water molecule allows it to form weak
  secondary bonds with other water molecules.

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Metallic Bonding

• Metals, having a low electronegativity, easily
  give up their valence electrons to form a sea
  of delocalized electrons surrounding their atoms.
  The positively charged atom cores that remain
  are bonded through negatively charged sea
• Aluminum atom with 3 valence electrons
• Valence electrons are no longer associated with
  any particular atom.

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Ionic and Hydrogen Bonding

• Ionic Bonding An atom donates its valence
  electron to a different atom of a different
  element. Each atom thus acquires an
  electromagnetic charge and ionically attract.
• Attraction between opposite charges NaCl

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Theory of Adhesion

• Types of Bonding
• Chemical
• Electrical
• Mechanical
• Theory of Adhesion (Surface Chemistry)
• Perfect fiber matrix interface requires that
  liquid resin wet or spread the fiber surface
• Contact angle formed by a drop of liquid on a
  surface is often taken as an indication of
  wettability measurement
• Surface Tension or Free EnergyForces on a
  molecule in bulk are balanced.Forces on a
  molecule at the surface are unbalanced. This
  unbalanced force gives rise to surface free
  energy.
• Work of adhesion WA is defined as the work
  required to separate two particles and defined in
  terms of surface energy
• WA ?A ?B ?AB ? surface free
  energy
• Wetting requires that the surface energy of the
  adherent (reinforcement) be greater than adhesive
  surface energy

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• ?

? lt 90º Good Wetting
? gt 90º No Wetting
? 90º Poor Wetting
? 0º for spontaneous wetting
Surface forces ?LV Liquid Vapor
phase ?SL Solid Liquid phase ?SV Solid Vapor
phase ?1 Liquid Surface Energy ?2 Solid
Surface Energy ?12 Free energy at L-S Interface

• ?LV and contact angle ? can be determined exp.
• In some cases, bond strength can be equated to WA

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• For spontaneous wetting
• e.g. Adhesive ?a 3.5 4.5 x 10-2
  N/m Fiber surface ?f 4.5 x 10-2 N/m
• Improper wetting may cause voids at the interface
  that lead to stress corrosion and result in
  cracking.
• Criteria for Better Wetting
• Surface must be free of foreign particles. This
  removes weak boundary layer or contaminants (H2O,
  organic vapor, nitrates, ketones, alcohols,
  amines)
• A large interfacial area of intimate contact
• Thermodynamically, a high surface-energy surface
  is the most conductive to good wetting,
  particularly if adhesive contains polar
  functional group.
• Surface energy of the adherent (reinforcement)
  should be greater than the adhesive surface
  energy (matrix).
• Creation or addition of chemical group
• Variation in surface topography (mechanical
  interlocking)

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Five Primary Adhesion Mechanism

• Adsorption and wetting
• Interdiffusion
• Electrostatic attraction
• Primary chemical bonding
• Mechanical interlocking

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Adsorption and Wetting

• Adsorption theory
• Ordinary dispersion of Van der Waals forces can
  be responsible for adhesive strength if
  sufficiently intimate contact is achieved
• Hydrogen bonding can enhance adhesion
• Primary chemical bonding may provide the links
  across the interface in some cases
• e.g. Secondary force interaction
• The attraction only due to dispersion
  forces
• Theoretical 100 MPa !!
• Experimental Strength of most joints
  much smaller
• Why
• Air voids, cracks, geometric defects acting as
  stress raisers when the joint is loaded.
• Impurities like H2O, organic vapor, nitrates,
  ketones, alcohol, and amines can weaken adhesion.

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Adsorption and wetting

• If two polymers are compatible, good bonding can
  be achieved.
• WA can not always be equated with bond strength
  since bond strength also contains energy
• For WA Wpeel, at low temperatures, high peel
  rate
• Surface Tension Data
• Substrate (reinforcement) Adhesive (Matrix,
  Liquid)
• Glass 560 mJ/m2 Polyester 35 mJ/m2
• Graphite 70 mJ/m2 Epoxy 43 mJ/m2
• Polyethylene 31 mJ/m2 P.E. lt Epoxy
• Can epoxy wet P.E.? -No

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Interdiffusion

• Mutual diffusion of the molecules at the
  interface forms a bond between two polymer
  surfaces. The requirement for such bonding is
  that both chain segments of polymer A and B
  should be mutually miscible or compatible.
• Miscibility or Solubility parameter
• Molecular Volume
• Cohesive Energy Density
• Similar values of S -gt miscible?
• Interdiffusion works well with
• Autohesion of elastomers
• Solvent welding of compativle amorphous plastics

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Interdiffusion

• Interdiffusion theory is good if
• Solubility parameters of the materials are
  similar
• One polymer is highly cross linked
• One polymer is crystalline
• One polymer is above its Tg

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Electrostatic Adhesion

• Acid-Base interaction
• Ionic Bonding
• Strength of the interface dependent on charge
  density
• Unlikely to make major contribution to the final
  bond strength
• Exception If ionic functional silanes (coupling
  agent in glass fiber) are used, the anionic
  functional groups may be attracted to an anion
  surface and vice versa.

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Primary (chemical) Bonding

• More important than secondary bonding. Although
  secondary bonding forces alone may result in
  adequate joint strength, additional presence of
  primary bonding my often increase the joint
  strength.
• Primary bonding is important to secure
  environmentally stable interface
• Ex. Coupling agent Glass Surface
• Polymer matrices Carbon Fiber
• Techniques to study chemical bonding of
  interface
• Laser
• X-ray photo electron spectroscopy (XPS)
• Secondary-ion mass spectroscopy
• Inelastic Electron Tunelling

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Mechanical Interlocking

• Interlocking of the adhesive into irregular rifts
  of the substrate surface is the key source of
  intrinsic adhesion.
• Generally not applicable.

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Mechanics of Composites
Micromechanics
Macromechanics
Mechanics of Materials
Fiber-Matrix interaction
Elasticity
Anisotropic (General)
Orthotropic (lamination theory)
E. Constant
Strength
Elastic Constants
Strength
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Micromechanics Approach

• Provides an understanding of the behavior of
  composites in terms of the properties and
  interactions of the fibers and matrix
• Interactions of fibers and matrix is examined on
  a microscopic scale
• Approximate models are used to simulate the
  microstructure of the composite and hence its
  average properties in terms of the properties
  of the constituents

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1
Longitude
Shear
Matrix
Transverse
2
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Micromechanics

• Mechanics of Material Approach (Prediction of
  Elastic Constants)
• Basic Assumptions
• Fibers are uniformly distributed throughout the
  matrix
• Perfect fiber-matrix bonding
• No voids in the matrix
• Applied loads are either parallel or normal to
  the fiber direction
• No residual stresses (stress-free initially)
• Both fiber and matrix are linearly elastic
• Consider an undeformed element,

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Macromechanics Approach

• The response of a fiber reinforced composites
  mechanical and thermal loads is examine on a
  mactoscopic scale.
• To design or predict, the behavior of a laminated
  structure on the average properties of the
  unidirectional material.
• These average properties include
• E1 longitudinal modulus
• E2 transverse modulus
• V12 major poisons ratio
• G12 in-plane shear modulus
• Several main strength values are required
• s1u longitudinal strength (both tensile and
  compressive)
• s2u transverse strength (both tensile and
  compressive)
• t12u shear strength

ply-1
0
0
45
-45
45
ply-2
90
Laminate
-45
ply-3
90
ply-4
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Prediction of Elastic Constants
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Mechanics of Materials models for the
determination of elastic constants
Property Determined
Applied Stresses
Deformations
Assumptions
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E1, Longitudinal modulus
Perfect bonding, Linear elastic, Force shared by
the fibers and matrix,
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Q What is the fraction of load carried by fibers
in a unidirectional continuous fiber lamina?
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Eg. E-glass Carbon Boron Epoxy 10x106 30x106
55x106 0.1x106
(A). E-glass/epoxy composite
(B). Carbon/epoxy
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E2, Transverse Modulus
Iso-stress (in series)
Deformations are additive,
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(No Transcript)
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G12, Shear Modulus
Assume Shear Stress, Shear Strain, Total
Shear deformation,
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12, Shear Modulus
(4)
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Refinements to Mechanics of Materials Approach
(RVE Representative Vol. Element) Hopkins and
Chamis (1988) / RVE / Book by Gibson / Jones
Note The E2, G12 expressions based on the
mechanics of materials approach are questionable
due to invalid assumptions. Agreement with
experiment is generally poor.
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It can be shown that the lower bound on E1 is
given by
Reference Mechanics of Composite Materials,
3.3.2. Variational Bounding Technique of
Elasticity, Robert M. Jones
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Direct Approaches
Various models of elastic inclusions in an
elastic matrix are used to obtain exact solutions
for the elastic constants. in many cases, the
solutions are highly complex and of limited
practical use. c degree of contiguity
extent of contact between fibers, c has more
effect on E2 and G12 than on E1.
Real Structure
Reference Mechanics of Composite Materials,
3.3.2. Variational Bounding Technique of
Elasticity, Robert M. Jones
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The Halpin-Tsai Equations Unidirectional Short
Fibers
The Halpin-Tsai eqns are simple approximate forms
of the generalized self-consistent micromechanics
solution developed by Hill. For oriented
reinforcements (fibers, flakes, and ribbons)
Very small/Negligible
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Elastic Constants 3D Randomly Oriented Short
Fiber
Randomly oriented short-fiber composites are
produced to obtain isotopic properties. Empirical
Equation
E11, E22 Longitudinal and transverse stiffness
for unidirectional oriented ply of the same fiber
aspect ratio and same fiber vol. fraction as the
randomly oriented discont. fiber. E11, E2
Halpin-Tsai Eqn.
2D- Random Orientation All fiber lie in 1-2
direction (no fibers lie in 3 direction)