Strength of Elastomers
Professor Joe Greene
CSU, CHICO
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Copyright Joseph Greene 2001
Strength of Elastomers
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Introduction
Initiation of Fracture
Threshhold of Strengths and Extensibilities
Fracture under Multiaxial Streses
Crack Propagation
Tensile Rupture
Repeated Stressing: Mechanical Fatigue
Surface Cracking by Ozone
Abrasive Wear
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Copyright Joseph Greene 2001
Initiation of Fracture
• Fracture is a highly selective process
– Only a small number of those molecules making up the test piece
actually undergo rupture.
• Questions
– Where and under what conditions does fracture begin?
– What laws govern the growth of a crack once it has been initiated?
• Initiation of fracture from flaws or points of weakness
– Applied stress is greatly magnified
– Fracture begins at such points
– Propagation of the crack is dependent on the load applied and the
geometry near the crack
• Rubber is viscoelastic
– Mechanical properties depend upon the rate of deformation
Copyright Joseph Greene 2001
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Initiation of Fracture
• Flaws and Stress risers
– Every solid body has flaws or points of weakness
• Inhomogenity of composition or structure
• Sharp corners, nicks, cuts, scratches….
– Stress is locally higher in these regions
• If higher than strength of the material, it will break.
– Stress concentration factor
• Ratio of the stress at the tip of a sharp flaw to the applied stress
– Equation 1
• Edge flaws are more serious stress raisers than enclosed flaws
of the same size.
• Figure 1. Tip versus enclosed crack.
• Figure 2. Distance away from crack.
• Figure 3. Fatigue lives
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Copyright Joseph Greene 2001
Initiation of Fracture
• Tensile Test Piece
– Thin strip of thickness, t, with a cut in one edge of depth,
l, is place in tension until it breaks.
• Figure 4
• Effect of cut in diminishing the total stored elastic energy, U,
can be calculated by
– Reduction in stored energy = kl2tU, where k = pi/(1+strain)1/2
• Tear Test Piece
– Test piece, Fig 5, has regions I in the arms that are in
simple extension and II that is undeformed.
– Work of fracture is GcA
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Copyright Joseph Greene 2001
Threshhold Strengths and Extensibilities
• Lake and Lindley researchers found that
– Minimum amount of mechanical energy is needed (about
50 J/m2) for a crack to propagate at all.
– Other researchers found range between 20-100 J/m2
– Threshold fracture energy, G0 is a function of Molecular
weight between crosslinks, Mc. G0 =  Mc 1/2
• Where  is a function of density of the polymer, the mass,
length, and effective flexibility of the monomer unit.
•  is found to be about 0.3 J/m2 (g/g-mole) -1/2
– For example, Mn=300,000, Mc =15,000, and , then G0 =25 J/m2
• Increased crosslinking leads to higher E and then higher tensile
strength which resists the fracture.
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Copyright Joseph Greene 2001
Fracture Under Multiaxial Stresses
• Few studies concern the fracture of elastomers under
complex stress conditions, though
• Compression and shear
– Elastomers do not fail along shear planes.
• Fractures develop at 45 to the direction of the shear (Fig 6)
– At right angles to the corresponding principle tensile stress and at a shear stress
equal to the tensile strength.
– General condition for rupture appears to be the attainment of a specific tensile
stress at the tip of an existing flaw.
• No case of fracture has occurred under uniform triaxial compression loading
when all compressive stresses are equal
– Under uniaxial compression, a breaking stress 8X as in tension by
growth of a crack in an oblique direction.
• Difficult to achieve uniaxial compression
• Instead, friction at the loaded surfaces of a thin compressed block prevents
elastomer from expanding laterally, a bulge develops and tears.
– Rubber block under compression is resistant to fracture, but
stiffness is reduced byCopyright
loss of
rubber in outer regions
Joseph Greene 2001
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Crack Propagation
• Crack propagation is widely different.
– 3 basic patterns of crack propagation correspond to elastomer type.
• Amorphous elastomers- SBR
– Exhibit simple tearing behavior: Once fracture starts, a tear propagates at rate
dependent upon strain energy release rate G and temperature, T.
• Crystallize on stretching- NR and Neoprene
– Tear strength is enhanced over a range of tear rates and temperatures
• Reinforced elastomers with 30% fillers- carbon black
– Particles cause an increase in tear strength and tensile strength by 10 fold over a
range of rates and temperatures of test.
– Dynamic (repeated) crack propagation
• Amorphous elastomers tear steadily at rates controlled by available energy,
G, for fracture
• Strain crystallizing elastomers do not tear continuously under small values of
G.
• Fig 19
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Copyright Joseph Greene 2001
Tensile Rupture
• Effects of Rate and Temperature
– Several relations are shown for breaking stress of unfilled SBR as
a function of rate of elongation. Fig 20
• Relationship forms parallel curves and into one Master Curve
– Fig 21- Strength at a given temperature is equal to the strength at another
temperature with a scale factor imposed. (In a log-log scale)
– Fig 22- Master curve (WLF relationship for polymers Equation 19) is based
upon reference temperature.
• Failure envelope for tensile rupture over range of T and rate of elongation
– Plot breaking stress against corresponding breaking extension.
– Yield a single curve, failure envelope, with a parabolic shape.
» Follow curve in an anticlockwise sense corresponds to the rate of extension
or to decreasing temperature
» At Lower extreme, breaking stress and elongation are small as a result of a
low rates of strain or at high temperatures.
» At Higher extreme, breaking stress and elongation are large as a result of a
high rates of strain or at low temperatures.
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Copyright Joseph Greene 2001
Tensile Rupture
• Effects of Degree of Crosslinking
– Breaking stress passes through a sharp maximum as
degree of crosslinking is increased from zero. Fig 24
• Due to changes in viscoelastic properties
– Failure envelops for degree of crosslinking
• Scale breaking elongation eb in terms of its maximum value
(dependent upon degree of crosslinking)
• Breaking stress is converted to a true stress at break rather than
the engineering stress. (Note: true stress is divided by actual
cross-sectional area during the test)
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Copyright Joseph Greene 2001
Tensile Rupture
• Strain-crystallizing elastomers
– Amorphous elastomers show steady fall in tensile
strength as temperature is raised.
– Strain-crystallizing elastomers show a rather sudden drop
at a critical temperature, Tc. Fig 26.
• Tc depends strongly on the extent of crystallization
• Sharp drop at critical temperature is due to failure of material to
crystallize at higher temperatures. It stays amorphous except at
the tip.
• Similar to similar drop at critical depth. Fig 27.
– Other aspects of Tc.
• The effect of a Tc is the same for compounds with fillers.
• Tc depends strongly on the type of crosslinking, being the
highest for long, polysulfidic crosslinks and the lowest for
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carbon-carbon crosslinks.
Copyright Joseph Greene 2001
Tensile Rupture
• Energy Dissipation and Strength
– General correlation between tensile strength and
temperature interval (T-Tg) as in the WLF equation, has
been well understood. T= test temp and Tg=glass
transition temp
– Example for polyurethane, Fig 28
• As temperature increases away from Tg the tensile strength
decreases linearly in log-log scale.
– Energy dissipation and strength, Fig 29
• Those materials that require the most energy to bring rupture
(strongest elastomers) are those in which the major part of
energy is dissipated before rupture causing heating or elastomer
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Copyright Joseph Greene 2001
Repeated Stressing: Mechanical Fatigue
• Fatigue failure
– Under repeated tensile deformations cracks appear in the
edges of the specimen and grow across it in an
accelerating way.
• Every time a deformation is imposed, energy G is available to
cause a strain energy to cause growth by tearing of a small nick
in the edge of the specimen.
• Corresponding growth step l obeys equation 22 (proportional
to G2), then the crack growth becomes
» l/l = (4k2 BU2)  n
» Where n is the number of times the deformation is imposed, k is a
numerical constant (about 2).
– The depth of crack after N strain cycles is obtained by integration, and
» l0-1 – l –1 = 4k2 BU2N
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» Fig 30 for Growth of and edge and Fig 31 for Fatigue life
Copyright Joseph Greene 2001
Repeated Stressing: Mechanical Fatigue
• Fatigue failure
– Examples of the dependence of fatigue life on an initial
cut size are shown in Figs. 3 and 31.
• Lives for test pieces which contain no deliberately introduced
cuts are represented by horizontal lines in Fig 3
– Interpreted as stepwise tearing from a hypothetical nick or flaw, 20
microns deep.
• Closely similar sizes of 20 microns are deduced natural flaws
for both strain-crystallizing and non crystallizing elastomers
• For non-crystallizing elastomers (SBR), the crack growth is
quite different over the main tearing region (Eqn 23)
– Different crack growth rate for strain crystallizing (NR) and
noncrystallizing (SBR) elastomers. Fig 32
» For SBR the fatigue life is more dependent on the size of the initial
flaw and the magnitude of the imposed deformation. So that
elastomers are generally longer-lived at small deformations and
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with no accidental cuts. Shorter lived under severe conditions.
Copyright Joseph Greene 2001
Repeated Stressing: Mechanical Fatigue
• Fatigue failure
– Fatigue life is drastically lowered at high temperatures as a result
of the sharp increase in the cut growth coefficient D as the internal
viscosity is decreased.
• The hysteresis associated with strain-induced crystallization is retained,
provided that the temp doesn’t get too high (100°C for NR) that
crystallization no longer occurs.
• Fatigue life for NR is not greatly affected by rise in temp
– Fatigue life is different between noncrystallizing and strain
crystallizing elastomers when stress is not relaxed to zero during
each cycle.
• Fig 33. Fatigue life for NR is greatly increased when minimum strain is
raised when minimum strain is increased from 0 to 100% because the
crystalline barrier to tearing at the tips of chance flaws does not then
disappear in the min strain state.
– The growth of flaws is virtually stopped unless the total applied strain is very
large (400-500%)
• For noncrystallizing elastomers, no comparable strengthening occurs15from
raising the minimum strain.
Copyright Joseph Greene 2001
Surface Cracking by Ozone
• In ozone environment,
– stretched samples of unsaturated elastomers develop
surface cracks which grow in length and depth until
failure.
• Even small cracks can cause reduction in strength and fatigue
life.
– Tensile stress necessary for an ozone crack is calculated
» from Eqn 6 __b=(GcE/l)1/2 for stress at break and
» Eqn 7 for extension eb=(Gc//lE)1/2
– Small amounts of fracture energy, G, of (0.1 J/m2) is needed for cracks
– Molecular scission occurs by reacting with the ozone.
» Example, Soft rubber, E=2 MPa, effective length, l, = 40 microns,
then Eqn 6 yields critical tensile stress of about 50 kPa and a
critical strain of about 5%. Cracks occur when stress is higher.
» As stress rises, more cracks form
» Note: many smaller cracks are less harmful than fewer large cracks
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Copyright Joseph Greene 2001
Abrasive Wear
• Mechanics of wear
– Abrasive wear consists of the rupture of small particles of
elastomer under action of frictional forces, when sliding takes
place between elastomer surface and a substrate.
• Suitable measure of the rate of wear is ration of A/
– A is the volume of rubber abraded away per unit normal load and per sliding
distance, and  is the coefficient of friction.
– Abradability= abraded volume per unit of energy dissipated in
sliding.
• Master curves for the dependence of abradability on the speed of sliding are
created by means of WLF relation (Eqns. 18,19)
• Abradability decreases with increasing speed, pass through a minimum, and
then rise again at high speeds as material becomes glasslike in response.
• Fig 34
• Carbon-filled elastomers are twice as large as for unfilled materials
– Reinforced material wear away faster due to intrinsic tear strength not being
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very high for unfilled materials.
Copyright Joseph Greene 2001