CHEM-E2200: Polymer blends and composites
Fracture and toughness in composites
Mark Hughes
12th October 2020
Toughness
“The worst sin in an engineering material is
not lack of strength or lack of stiffness,
desirable as these properties are, but lack of
toughness, that is to say, lack of resistance to
the propagation of cracks”
J.E. Gordon, The New Science of Strong Materials
Tension vs compression
• In most structures there is the
need to carry tensile as well as
compressive loads
• Brittle materials are okay in
compression (mainly) as cracks are
not “opened”
• Think of how, for example,
masonry (brick, stone) is used in
construction Tension:
The Menai suspension bridge, Wales
Compression:
A Roman arch
Is toughness important?
Catastrophic failure!
WW II Liberty ship
Are tough materials always tough and vice
versa?
• Lower the temperature and certain steels can become brittle
and in some cases can lead to catastrophic failure (as in the
case of the Liberty ships – the failure changed from ductile to
brittle when the temperature dropped in winter)
• Brittle materials such as glass, ceramics and certain polymers
are intrinsically brittle but can be tough if combined
Properties of cracks
Crack opening modes
Cracks and “crack-like” defects
• All real materials contain cracks or crack-like defects at
some scale
• These could be macroscopic cracks or “stress
concentrators” or “stress risers” such a holes or sharp
changes in section
– The failure of the Liberty ships initiated at the corners of
hatches (openings in the decks)
• Or they could be microscopic cracks
• There will be some kind of cracks or discontinuities
(changes in section or in material properties) in all
forms of material. Here cracks can initiate and
propagate
What’s wrong with this picture?
De Havilland Comet circa 1953
1950s de Havilland comet crashes
• Failure initiated at the ‘sharp’ corner of the window openings: large stress concentrations
(http://lessonslearned.faa.gov/ll_main.cfm?TabID=1&LLID=28&LLTypeID=2#null)
1950s de Havilland comet crashes
Stress concentrations
caused by the “sharp”
corners of the windows
initiated failure
http://aerospaceengineeringblog.com/dehavilland-comet-crash/
What is the effect of a crack?
• These cracks result in
localised stress
concentrations, the
magnitude of which depend
upon the size and shape of
the crack
What is the effect of a crack?
• If the stress concentrations are
high enough, the material near
the crack-tip may fail. Under
certain conditions a crack may
propagate catastrophically,
leading to sudden failure of the
material
• The crack-tip may, therefore,
be viewed as a mechanism
whereby local stresses in the
material are raised sufficiently
for fracture to occur
Cracks
• Stress concentration is
dependent upon the shape of
the crack
• Can be modelled as an ellipse
• As the crack tip radius
approaches zero (i.e. very
sharp – ratio of major to minor
axis is high) then the
(Source: Piggott, 1980)
theoretical stress concentration
approaches infinity a
max 1 2
b
Properties of heterogeneous
materials: crack-blunting and
crack-deflection
More about cracks…
(Cook & Gordon 1964)
(Source: Piggott, 1980)
Crack-stopping mechanisms
Interface
• Composites contain interfaces
• Wood contains multiple interfaces at several hierarchical levels!
Fracture and energy
Toughness of materials
(Source Hull and Clyne 1996)
Energy & fracture
• To break a material you need to do work
on it! In other words you need to supply
energy
• When load a material it causes a deformation (work = force x
distance)
• The stored ‘strain energy’ is available to propagate a crack
• Think of a ‘longbow’ – the string is pulled back with the arrow and bends
the bow. As the string is released the stored strain energy in the bow is
converted to kinetic energy in the arrow
• Or springs…
• If you need to do a lot of work to propagate a crack then the
material is ‘tough’
Energy & fracture
• Another way of looking at it is that if the material can “absorb”
large amounts of energy when fracturing then it is likely to be
tough
• If the material can absorb more energy when a crack advances
than can be supplied by the stored strain energy (change in
potential), then the crack will stop advancing
Measuring energy absorption during fracture is a
convenient method of measuring the toughness of a
material. This is why ‘impact tests’ such as the ‘Charpy test’
are so popular
Measurement of toughness
• “Charpy” or “Izod” tests
provide a measure to
toughness under impact
conditions
• Work of fracture measured
by loss of energy of a
swinging pendulum
• Impact “strength” expressed
as energy absorbed by
specimen over fracture
surface area
The Charpy impact test
Stress concentrations and energy
• So, cracks create stress concentrations in a material
that can raise the local stress sufficiently to cause
failure
• However, energy is needed to ‘drive’ the crack
• So, both stress and energy are important in fracture
• In 1920 A.A. Griffiths proposed a thermodynamic
explanation for fracture and started the science of
‘fracture mechanics’
Griffiths and fracture mechanics
• Griffiths (1920) linked the failure stress 1/ 2
( F ) of a material with the energy 2 S E
required to create new crack surfaces F (1)
(surface energy for truly brittle
material) and, ac, the critical crack ac
length (1)
• This was later extended to include E is Young’s modulus
tougher materials. In these, the surface 2 S is the work of fracture
energy term ( S ) is supplemented by ( S is the surface energy)
other energy absorption mechanisms
(see later)
• The energy release rate, G, is derived 2 .a
from the Griffith’s equation (2) G (2)
• The fracture energy (Gc) analogous to S
E 1/ 2
in the Griffith’s equation (3) GC E
F (3)
a
Equivalence of stress based and energy based
fracture criteria
A constant K, the stress intensity factor (units of
MN m-3/2) characterises the crack-tip stress-strain
conditions:
GK E 2
(in plane stress)
G K 1 v
2 2
E (in plane strain)
Where: v is Poisson’s ratio
Stress concentrations - I
• Toughness may be regarded as the resistance a
material possesses to the propagation of cracks or
crack-like defects which might ultimately lead to
failure
• Cracks may, for example, be macroscopic, ‘stress
raisers’ such as bolted joints, or sharp changes in
section, or alternatively pre-existing crack-like defects
in the material itself. These cracks result in localised
stress concentrations, the magnitude of which depend
upon the size and shape of the crack
Stress concentrations - II
• If the stress concentrations are high enough, the
material in the vicinity of the crack-tip may fail. Under
certain conditions, a crack may propagate
catastrophically, leading to sudden failure of the
material
• The crack-tip may, therefore, be viewed as a
mechanism whereby local stresses in the material are
raised sufficiently for fracture to occur
Energy absorption - I
• However, for the crack to propagate, it must be
energetically favourable for it to do so
• The energy to drive the crack forward is provided by
the release of stored strain energy in the material,
together with any external work done by the loading
system
• Therefore, a material that possesses mechanisms
whereby significant amounts of energy can be
absorbed as the crack advances or if, by some
contrivance, the stress concentration at the crack-tip
can be relieved, then the material is likely to be tough
Energy absorption - II
• Brittle materials such as glass have little means of
energy absorption or crack-blunting and hence fail in a
catastrophic manner, exhibiting low fracture energies
of around 0.01 kJ/m2
• Ductile metals such as mild steel, on the other hand,
absorb large quantities of energy by plastic
deformation. Typically, tough engineering materials
such as steel exhibit fracture energies of around 100
kJ/m2
Toughness of natural fibre reinforced
composites
80
Charpy impact strength (kJ m-2)
60
hemp reinforcement
hemp trendline
40 jute reinforcement
CSM reinforcement
jute trendline
20
0
0 10 20 30 40 50
fibre volume fraction (%)
Comparison of un-notched Charpy impact strength.
Jute, hemp and C.S.M. glass fibre reinforced laminates
The “Cook-Gordon” crack
stopping/blunting/deflection mechanism
• Stress field ahead of advancing crack, “opens up” an interface
• Transverse stress about 20% of axial stress
(Cook and Gordon, 1964)
Energy absorbing processes in composites
• Several energy absorbing mechanisms have been identified.
These are:
– Matrix deformation and fracture
– Fibre fracture
– Interfacial debonding
– Frictional sliding and fibre pull-out
• The contribution that each of the energy absorbing
mechanisms makes to the overall toughness of the composite
varies, depending upon the composite system involved and
the properties of the phases
Matrix deformation & fracture
• With brittle thermoset polymers, the contribution from
matrix deformation and fracture to the overall fracture
energy of the composite is likely to be small. Typically,
fracture energies of thermosetting polymers are of the order
of 0.1 kJ/m2
• The fracture energy of thermoplastic polymers such
polypropylene, or polyethylene are greater
Fibre fracture I
• Brittle fibres such as glass exhibit very low fracture energies
of the order 0.01 kJ/m2. The contribution to the overall work
of fracture of the composite is likely, therefore, to be small
• Wood fibres can, however, exhibit high works of fracture. It
has been observed that wood fibres can deform in a ‘pseudo-
plastic’ manner, due to the microfibril angle in the S2 layer.
This results in shear failure in the fibre cell wall, leading to
energy absorption. This mechanism is believed to account fro
up to 90% of the work of fracture of wood across the grain
(10-30 kJ/m2)
Fibre fracture II
• The work of fracture of the wood cell wall material (i.e. not
including the plastic deformation – the so-called “intrinsic
toughness”) has been reported to be between <0.35 and 3.45
kJ/m2 depending upon whether it is measured along or across
the fibre axis
• Thus, fibre fracture could, potentially, contribute fairly
significantly to the toughness of a wood fibre reinforced
composite
Interfacial debonding
• The debonding energy in composites is generally quite small,
~0.01 kJ/m2 and the resulting contribution to the overall work
of fracture is generally low (~0.5 kJ/m2). As discussed above
• If the interfacial fracture energy is increased too much,
debonding is prevented (i.e. the interface becomes too
strong) and this will lead to a reduction in the crack stopping /
blunting capacity
Fibre pull-out
• Frictional sliding and fibre pull-out as the fibre is withdrawn
from the matrix socket during fracture
• Potentially, this mechanism can absorb large amounts of
energy (of the order of 100 kJ/m2 if the interfacial frictional
forces are large and the pull-out length of the fibre are high
as is the case in glass fibre reinforced composites)
• Frictional energy dissipation during pull-out is dependent
upon interfacial roughness, contact pressure and sliding
distance
Fracture surfaces
Natural fibre Glass fibre
Fibre pull-out
Summary
• For engineering materials, adequate toughness is
essential
• Cracks and crack-like defects raise local stresses that
can lead to local failure
• Interfaces act as “crack-stopping” mechanisms
• If there is sufficient (strain) energy the crack can
propagate unstably, leading to catastrophic failure
• Composites employ different energy absorbing
mechanisms
Further reading & resources
• Ashby, M.F., Easterling, K.E., Harrysson, R. and Maiti, S.K. (1985). The
Fracture Toughness of Woods. Proc. R. Soc. Lond. A, 398: 261-280.
• Bailey C. Green Composites (Ebrary- through Nelli)
• Cook, J. and Gordon, J.E. (1964). A Mechanism for the Control of Crack
Propagation in All-Brittle Systems. Proc. Roy. Soc. Lond. A, 282: 508-520
• Dinwoodie J.M. (2000). Timber: its nature and behaviour
• Gordon J.E. The New Science of Strong Materials (Chapter 5)
• Griffith, A.A. (1920). The Phenomenon of Rupture and Flow in Solids.
Phil. Trans. R. Soc. Lond. A, 221: 163-198.
• Hull, D. and Clyne, T.W. (1996). An Introduction to Composite Materials.
Cambridge University Press, Cambridge, UK.
Further reading & resources
• Jeronimidis, G., (1980). The Fracture Behaviour of Wood and the
Relations Between Toughness and Morphology. Proc. R. Soc. Lond. B, 208:
447-460
• Morten Rask, M., Madsen, B., Sørensen, B.F., Fife, J.L., Martyniuk, K. and
Lauridsen, E.M. (2012). In situ observations of microscale damage
evolution in unidirectional natural fibre composites. Composites: Part A
43, 1639–1649
• Piggott, M.R. (1980). Load-Bearing Fibre Composites. Pergamon, Oxford
• Reiterer, A, Lichtenegger, H., Fratzl, P. Stanzl-Tschegg, S. E. (2001)
Deformation and energy absorption of wood cell walls with different
nanostructure under tensile loading, J. Mater. Sci. 36 4681 – 4686
