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Ecture 3.1: Low Stiffness in Polymers: Two Types of Polymers

The document discusses stiffness in polymers and composites. Polymers can have either a thermoplastic or thermoset backbone structure, which influences their stiffness. Stretching polymers increases their chain orientation and stiffness. Composites gain stiffness from the rule of mixtures, depending on the fiber fraction and properties of the fiber and matrix materials. Shape and dimensions influence the stiffness of structures like beams, ties and shafts under different loading modes through their second moment of area.

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Thomas Van Kuik
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35 views4 pages

Ecture 3.1: Low Stiffness in Polymers: Two Types of Polymers

The document discusses stiffness in polymers and composites. Polymers can have either a thermoplastic or thermoset backbone structure, which influences their stiffness. Stretching polymers increases their chain orientation and stiffness. Composites gain stiffness from the rule of mixtures, depending on the fiber fraction and properties of the fiber and matrix materials. Shape and dimensions influence the stiffness of structures like beams, ties and shafts under different loading modes through their second moment of area.

Uploaded by

Thomas Van Kuik
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as DOCX, PDF, TXT or read online on Scribd
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Lecture 3

Lecture 3.1: Low stiffness in polymers


Polymers: chain-like structures of repetitive units bonded along C-C backbone

Key features:

- The composition of the repetitive unit (the monomer)


- The number of linked units (the molecular weight)
- a linear backbone or a crosslinked backbone

Two types of polymers

Thermoplastics: the chains are connected through weak van der Waals forces

Thermosets: the chains are connected through weak van der Waals forces and strong covalent bonds
called crosslinks

Because of entropy most polymers like their molecules to coil up in a random structure. Now,
deformation of such a polymer does proceed via the rotation of segments of the molecule.

Amorphous (disordered) polymers: transparent

Semi-crystalline (ordered) polymers: translucent

Stretching polymers

Unstretched: more anisotropic

Stretched: chain orientation, more anisotropy and higher stiffness

The modulus of polymers

The modulus of polymers depends more on average molecular alignment than on composition.

In crosslinked polymers composition and crosslinking density have relative high impact.

The structure and therefore the elastic properties can be anisotropic

The consequences for the temperature dependence of E-modulus of polymers


Lecture 3.2: The mid-high stiffness in hybrids (composites)
Hybrid properties

Properties of composites are bound by the property values of the constituents

UD fibre reinforced matrices

Under an external axial load parallel to the fibres the strain in the fibres is the same as the strain in
the matrix

The forces required to strain the fibres F fibres = ff * A0 * Ef * , where ff is fibre fraction

The force required to strain the matrix Fmatrix = (1-ff) * Ao * Em * 

The total force Fcompos = Ffibres + Fmatrix

Hence: Fcompos / A0 = ff * Ef *  + (1-ff) * Em * 

or

Under an external axial load perpendicular to the fibres the stress in the fibre is the same as the
stress in the matrix

By analogous analysis

Changing performance by going porous

Lecture 3.3: Stiffness-limited design


Separating the effects of shape (+ dimensions) and material on stiffness of the product

Three common loads of modes of loading

- Tie with a circular cross-section loaded in tension


- Beam with a rectangular cross-section loaded in bending
- Shaft of circular cross-section loaded in torsion
Stiffness of a tie rod loaded in tension

Relation between load F, deflection  and stiffness S

Shape of cross-section does not matter because the stress is uniform across the section

Buckling of columns and plates under axial compression

If sufficiently slender, an elastic column or plate, loaded in compression fails by elastic buckling at a
critical load

Value of n depends on the end constraints of the beam

Elastic bending of beams

Curvature of initially straight axis

Stress caused by bending moment in a beam with a given Young’s modulus

Second moment of area

Shape matters: the material resists better bending the further is from the neutral axis

I characterizes the bending resistance of the section (includes the size and the shape)

Elastic stiffness of a beam under transverse loading

C1 is the only value that depends on the beam supports and the distribution of the load

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