In materials science, fracture toughness is a property which describes the ability of
a material containing a crack to resist fracture, and is one of the most important properties
of any material for many design applications. The linear-elastic fracture toughness of a
material is determined from the stress intensity factor at which a thin crack in the material
begins to grow. It is denoted KIc and has the units of or . Plastic-elastic fracture
toughness is denoted by JIc, with the unit of J/cm2 or lbf-in/in2, and is a measurement
of the energy required to grow a thin crack. The subscript Ic denotes mode I crack opening
under a normal tensile stress perpendicular to the crack, since the material can be made
deep enough to stand shear or tear. Fracture toughness is a quantitative way of
expressing a material's resistance to brittle fracture when a crack is present. If a material
has much fracture toughness it will probably undergo ductile fracture. Brittle fracture
is very characteristic of materials with less fracture toughness.
Fracture mechanics, which leads to the concept of fracture toughness, was broadly based on
the work of A. A. Griffith who, among other things, studied the behavior of cracks in
brittle materials. A related concept is the work of fracture
which is directly proportional to , where is the Young's modulus of the material. Note
that, in SI units, is given in J/m2.
Example values The following table shows some typical values
of fracture toughness for various materials: Crack growth as a stability problem
Consider a body with flaws that is subject to some loading; the stability of the crack
can be assessed as follows. We can assume for simplicity that the loading is of constant
displacement or displacement controlled type; we can also simplify the discussion by characterizing
the crack by its area, A. If we consider an adjacent state of the body as being one with
a broader crack, we can then assess strain energy in the two states and evaluate strain
energy release rate. The rate is reckoned with respect to the change
in crack area, so if we use U for strain energy, the strain energy release rate is numerically
dU/dA. It may be noted that for a body loaded in constant displacement mode, the displacement
is applied and the force level is dictated by stiffness of the body. If the crack grows
in size, the stiffness decreases, so the force level will decrease. This decrease in force
level under the same displacement level indicates that the elastic strain energy stored in the
body is decreasing—is being released. Hence the term strain energy release rate which
is usually denoted with symbol G. The strain energy release rate is higher for
higher loads and broader cracks. If the strain energy so released exceeds a critical value
Gc, then the crack will grow spontaneously. For brittle materials, Gc can be equated to
the surface energy of the new crack surfaces; in other words, in brittle materials, a crack
will grow spontaneously if the strain energy released is equal to or more than the energy
required to grow the crack surface(s). The stability condition can be written as
elastic energy released = surface energy created. If the elastic energy released is less than
the critical value, then the crack will not grow; equality signifies neutral stability
and if the strain energy release rate exceeds the critical value, the crack will start growing
in an unstable manner. For ductile materials, energy associated with plastic deformation
has to be taken into account. When there is plastic deformation at the crack tip the energy
to propagate the crack may increase by several orders of magnitude as the work related to
plastic deformation may be much larger than the surface energy. In such cases, the stability
criterion has to be restated as elastic energy released = surface energy +
plastic deformation energy. Practically, this means a higher value for
the critical value Gc. From the definition of G, we can deduce that it has dimensions
of work /area or force/length. For ductile metals GIc is around 50–200 kJ/m2, for brittle
metals it is usually 1–5 and for glasses and brittle polymers it is almost always less
than 0.5. The problem can also be formulated in terms
of stress instead of energy, leading to the terms stress intensity factor K and critical
stress intensity factor Kc. These Kc and KIc quantities are commonly referred to as fracture
toughness, though it is equivalent to use Gc. Typical values for KIcare 150 MN2 for
ductile metals, 25 for brittle ones and 1–10 for glasses and brittle polymers. Notice the
different units used by GIc and KIc. Engineers tend to use the latter as an indication of
toughness. Conjoint action
There are number of instances where this picture of a critical crack is modified by corrosion.
Thus, fretting corrosion occurs when a corrosive medium is present at the interface between
two rubbing surfaces. Fretting results from the disruption of very small areas that bond
and break as the surfaces undergo friction, often under vibrating conditions. The bonding
contact areas deform under the localised pressure and the two surfaces gradually wear away.
Fracture mechanics dictates that each minute localised fracture has to satisfy the general
rule that the elastic energy released as the bond fractures has to exceed the work done
in plastically deforming it and in creating the fracture surfaces. This process is enhanced
when corrosion is present, not least because the corrosion products act as an abrasive
between the rubbing surfaces. Fatigue is another instance where cyclical
stressing, this time of a bulk lump of metal, causes small flaws to develop. Ultimately
one such flaw exceeds the critical condition and fracture propagates across the whole structure.
The fatigue life of a component is the time it takes for criticality to be reached, for
a given regime of cyclical stress. Corrosion fatigue is what happens when a cyclically
stressed structure is subjected to a corrosive environment at the same time. This not only
serves to initiate surface cracks but actually modifies the crack growth process. As a result
the fatigue life is shortened, often considerably. Stress-corrosion cracking
This phenomenon is the unexpected sudden failure of normally ductile metals subjected to a
constant tensile stress in a corrosive environment. Certain austenitic stainless steels and aluminium
alloys crack in the presence of chlorides, mild steel cracks in the presence of alkali
and copper alloys crack in ammoniacal solutions. Worse still, high-tensile structural steels
crack in an unexpectedly brittle manner in a whole variety of aqueous environments, especially
chloride. With the possible exception of the latter, which is a special example of hydrogen
cracking, all the others display the phenomenon of subcritical crack growth; i.e. small surface
flaws propagate under conditions where fracture mechanics predicts that failure should not
occur. That is, in the presence of a corrodent, cracks develop and propagate well below KIc.
In fact, the subcritical value of the stress intensity, designated as KIscc, may be less
than 1% of KIc, as the following table shows: The subcritical nature of propagation may
be attributed to the chemical energy released as the crack propagates. That is,
elastic energy released + chemical energy = surface energy + deformation energy.
The crack initiates at KIscc and thereafter propagates at a rate governed by the slowest
process, which most of the time is the rate at which corrosive ions can diffuse to the
crack tip. As the crack advances so K rises. Finally it reaches KIc, whereupon swift fracture
ensues and the component fails. One of the practical difficulties with SCC is its unexpected
nature. Stainless steels, for example, are employed because under most conditions they
are passive; i.e. effectively inert. Very often one finds a single crack has propagated
whiles the left metal surface stays apparently unaffected.
Toughening Mechanisms Intrinsic Mechanisms
Intrinsic toughening mechanisms are processes which act ahead of the crack tip to increase
the material's toughness. These will tend to be related to the structure and bonding
of the base material, as well as microstructural features and additives to it. Examples of
mechanisms include crack deflection by secondary phases, crack bifurcation due to fine grain
structure and modification to the grain boundaries, and crack meandering by pores in the material.
Any alteration to the base material which increases its ductility can also be thought
of as intrinsic toughening. Extrinsic Mechanisms
Extrinsic toughening mechanisms are processes which act behind the crack tip to resist its
further opening. Examples include fibre/lamella bridging, where these structures hold the
two fracture surfaces together after the crack has propagated through the matrix, crack wedging
from the friction between two rough fracture surfaces, microcracking, where smaller cracks
form in the material around the main crack, relieving the stress at the crack tip by effectively
increasing the material's compliance, and transformation toughening.
"Transformation toughening" is a phenomenon whereby a material undergoes one or more martensitic
phase transformations which result in an almost instantaneous change in volume of that material.
This transformation is triggered by a change in the stress state of the material, such
as an increase in tensile stress, and acts in opposition to the applied stress. Thus
when the material is locally put under tension, for example at the tip of a growing crack,
it can undergo a phase transformation which increases its volume, lowering the local tensile
stress and hindering the crack's progression through the material. This mechanism is exploited
to increase the toughness of ceramic materials, most notably in Yttria-stabilized zirconia
for applications such as ceramic knives and thermal barrier coatings on jet engine turbine
blades. Fracture toughness testing methods
Fracture toughness is a critical mechanical property for certain applications. There are
several types of test used to measure fracture toughness of materials.
Determination of plane strain fracture toughness, KIc
When a material behaves in a linear elastic way prior to failure, such that the plastic
zone is small compared to the specimen dimension, a critical value of Mode-I stress intensity
factor can be an appropriate fracture parameter. This method provides a quantitative measure
of fracture toughness in terms of the critical plane strain stress intensity factor. The
test must be validated once complete to ensure the results are meaningful. The specimen size
is fixed, and must be large enough to ensure plane strain conditions at the crack tip.
This limits the product forms to which the test can be applied. In the 1960s, it was
postulated that small specimens or thin sections fail under plane stress conditions, and that
‘‘plane strain fracture’’ occurs in thick sections. The ASTM E 399 test method
reflects this viewpoint. Over the years, it has been taken as an indisputable fact that
toughness decreases with increasing specimen size until a plateau is reached. Specimen
size requirements in ASTM E 399 are intended to ensure that KIc measurements correspond
to the supposed plane strain plateau. The specimen size requirements in this standard
are far more stringent than they need to be to ensure predominately plane strain conditions
at the crack tip. The real key to a K-based test method is ensuring that the specimen
fractures under nominally linear elastic conditions. That is, the plastic zone must be small compared
to the specimen cross section. Consequently, the important specimen dimensions to ensure
a valid K test are the crack length a and the ligament length W – a, not the thickness
B. Four specimen configurations are permitted by the current version of E 399: the compact,
SE(B), arc-shaped, and disk-shaped specimens. Specimens for KIc tests are usually fabricated
with the width W equal to twice the thickness B. They are fatigue precracked so that the
crack length/width ratio lies between 0.45 and 0.55. Thus, the specimen design is such
that all of the key dimensions, a, B, and W− a, are approximately equal. This design
results in the efficient use of material, since the standard requires that each of these
dimensions must be large compared to the plastic zone.
Determination of tear resistance The tear test provides a semi-quantitative
measure of toughness in terms of tear resistance. This type of test requires a smaller specimen,
and can therefore be used for a wider range of product forms. The tear test can also be
used for very ductile aluminium alloys, where linear elastic fracture mechanics do not apply.
Fracture toughness of AISI steel The fracture toughness of AISI 4340 steel
has been determined by several methods, i.e.Jr curve,δr curve, Kr curve, stretch zone size
measurements non-linear energy method of Poulose et al. and by a new procedure proposed recently
by Banerjee. Compact tension specimens with TL orientation have been used. All the specimens
used satisfied the ASTM E813 test size requirements. Applicability of various fracture toughness
estimation procedures like Hanhn and Rosenfield, Rolfe and Barsom and equivalent energy rate
method of Bucci et al. have been examined. These values have been compared with true
fracture toughness of the material obtained by ASTM E399 test procedure.
Comparison of various conventional test methods indicate multiple specimen curve method gives
most consistent results and these values are within +15% of the true fracture toughness
value. Out of all estimation procedures Rolfe and Barsom's method appears to be best, giving
number within +8% of the true fracture toughness value. Non-linear energy method was found
to give a fracture toughness value consistent with true fracture toughness of the material
Other methods for determining fracture toughness C1161 Test Method for Flexural Strength of
Advanced Ceramics at Ambient Temperature C1322 Practice for Fractography and Characterization
of Fracture Origins in Advanced Ceramics E4 Practices for Force Verification of Testing
Machines E112 Test Methods for Determining Average
Grain Size E177 Practice for Use of the Terms Precision
and Bias in ASTM Test Methods E337 Test Method for Measuring Humidity with
a Psychrometer E399 Test Method for Plain-strain Fracture
Toughness of Metallic Materials E691 Practice for Conducting an Interlaboratory
Study to Determine the Precision of a Test Method
E740 Practice for Fracture Testing with Surface-Crack Tension Specimens
E1823 Terminology Relating to Fatigue and Fracture Testing
IEEE/ASTM SI 10 Standard for Use of the International System of Units
See also Stress intensity factor
Puncture resistance Fracture mechanics
Brittle-ductile transition zone Charpy impact test
Impact Izod impact strength test
Toughness of ceramics by indentation Shock
Stress corrosion cracking
References
Other references Anderson, T. L., Fracture Mechanics: Fundamentals
and Applications. Davidge, R. W., Mechanical Behavior of Ceramics.
Lawn, B., Fracture of Brittle Solids. Knott, Fundamentals of Fracture Mechanics.
Foroulis, Environmentally-Sensitive Fracture of Engineering Materials.
Suresh, S., Fatigue of Materials. West, J. M., Basic Corrosion & Oxidation,
chap.12. Green, D. J.; Hannink, R.; Swain, M. V.. Transformation
Toughening of Ceramics, Boca Raton: CRC Press. ISBN 0-8493-6594-5.
http:www.sv.vt.eduMSE2094_NoteBookexperwww/fractough.html http:www.springerlink.comv2m7u4qm53172069/fulltext.pdf
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