Chapter 3 Rubber Elasticity resilient but weak to heat
Metals are strong but weak to corrosion/fatigue: Ceramics stiff but brittle.
Polymers are light, cheap, high strength/wt, tough, corrosion- resistant, insulating, low friction, ---
mechanical property
mechanical response of a material to the applied stress [load]
response of a polymer depends on
chemical structure ~ PE, PS, ---
physical structure ~ crystallinity, aged, ---
temperature
upon small stresses
viscoelastic deformation Chapt 20
failure [fracture] Chapt 23
deformations of the bond lengths and angles
uncoiling of the chains
slippage of the chains
scission of the chains
j = direction
by equilibrium (no rotation), 6 3
Fig 19.1 p470
principal stresses and principal axes
if all t’s are 0
normal stresses are principal stresses
x1, x2, and x3 are principal axes
two axes on free surface are principal
hydrostatic and deviatoric stress
deviatoric stress (component)
L0dL
g
e and e: more generally
engineering [nominal] strain e = DL/L0
true strain de = dL/L
engineering [nominal] stress s = F/A0
true stress s = F/A
Ch 19 sl 7
L0DL
uniaxial tension
uniaxial compression
simple shear ~ torsion
plane stress
bending or flexure plane e
x2
x1
x3
e = s s s ~ compliance
81 36 21 13 9 5 2
2 constants for isotropic solids
Ch 19 sl 9
equilibrium symmetry in material
s1 = E e1
E = Young’s modulus [, ]
modulus = resistance to deformation, stiffness
e = D s
for rubbers, n = 0.5 ~ no volume change
for plastics, n ~ 0.4
x2
x1
x3
L0DL
t6 = G g6
G = shear modulus []
e1 = s1/E – n e2 – n e3
= s1/E – n s2/E – n s3/E
= (1/E) [s1 – n (s2 + s3)]
e2 =
e3 =
no interaction betw normal and shear
e2 = s2/E
dilatation or volume strain D
p = K D K = bulk modulus (= resistance to volume change)
D = b p b = compressibility
relations between elastic constants
Only 2 of 4 (E, G, K, n) are independent.
e.g., E = 3G, K = for elastomers
s2
s1
s3
s(1) = E e(1) (Hooke’s law)
e2 = − n e1
anisotropic solid (fiber, composite) ~ orientation-dependent
E11 ≠ E22; n12 ≠ n31
It is hard to express the real mechanical response with a constitutive equation.
s
e
semicrystalline polymers
crosslinked polymers
change in length
estimated by raman, IR, --
rather low, due to intermolecular interaction? should be small
Ch 19 sl 16
c = lattice parameter
drawn fiber
Fig 19.8
Fig 19.6
460 GPa
Ch 19 sl 18
Deformation of semicrystalline polymers
two groups
E(crystal) >> E(matrix)
E(crystal) ≈ E(matrix)
Ch 19 sl 20
- crystal, amorphous for semicrystalline