Fracture toughness wikipedia, the free encyclopedia

4/1/2016 Fracture toughness Wikipedia, the free encyclopedia
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Fracture toughness
From Wikipedia, the free encyclopedia
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 linearelastic 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
. Plasticelastic fracture toughness is denoted by JIc, with the unit of J/cm2 or lbfin/in2, and is a
measurement of the energy required to grow a thin crack.
The subscript I 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 (mode II) or tear (mode III).
Fracture toughness is a quantitative way of expressing a material's resistance to brittle fracture when a crack
is present. If a material has high fracture toughness it will probably undergo ductile fracture. Brittle fracture
is very characteristic of materials with low fracture toughness.[1]
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.[2] Note that, in SI units, is given in J/m2.
Contents
1 Example values
2 Crack growth as a stability problem
3 Conjoint action
4 Stresscorrosion cracking (SCC)
5 Toughening Mechanisms
5.1 Intrinsic Mechanisms
5.2 Extrinsic Mechanisms
6 Fracture toughness testing methods
6.1 Determination of plane strain fracture toughness, KIc
6.2 Determination of tear resistance (Kahn tear test)
6.3 Fracture toughness of AISI steel

6.4 Other methods for determining fracture toughness
7 Strain Energy Release Rate
8 See also
9 References
10 Other references
Example values
The following table shows some typical values of fracture toughness for various materials:
Material type Material KIc (MPa · m1/2)
Metal
Aluminum alloy (7075) 24
Steel alloy (4340) 50
Titanium alloy 44–66
Aluminum 14–28
Ceramic
Aluminum oxide 3–5
Silicon carbide 3–5
Sodalime glass 0.7–0.8
Concrete 0.2–1.4
Polymer
Polymethyl methacrylate 0.7–1.6
Polystyrene 0.7–1.1
Composite
Mullitefibre composite 1.8–3.3[3]
Silica aerogels 0.0008–0.0048[4]
Crack growth as a stability problem
Consider a body with flaws (cracks) 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 (such as loading with a screw jack); 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 (area A+dA), 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 (or compliance) 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 (strain) 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 (two) 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 (as occurs most often in metals) 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 (or energy) /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 (or KI for mode I) and critical stress intensity factor Kc (and KIc). These Kc and KIc (etc.) quantities
are commonly referred to as fracture toughness, though it is equivalent to use Gc. Typical values for KIcare
150 MN/m3/2 for ductile (very tough) 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 (in the absence of corrosion) 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 (very tiny) 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 (see below)
actually modifies the crack growth process. As a result the fatigue life is shortened, often considerably.
Stresscorrosion cracking (SCC)
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 (boiler cracking) and copper alloys crack
in ammoniacal solutions (season cracking). Worse still, hightensile 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 (usually smoothly) 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:
Alloy
KIc (
)
SCC
environment
KIscc (
)
13Cr steel 60 3% NaCl 12
18Cr8Ni 200 42% MgCl2 10
Cu30Zn 200 NH4OH, pH7 1
Al3Mg7Zn 25
aqueous
halides
5
Ti6Al4V 60 0.6M KCl 20
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
(because crack size appears in the calculation of stress intensity). 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.[5]
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.[6]
"Transformation toughening" is a phenomenon whereby a material undergoes one or more martensitic
(displacive, diffusionless) 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
Yttriastabilized zirconia for applications such as ceramic knives and thermal barrier coatings on jet engine
turbine blades.[7]
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 ModeI 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 Kbased 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), arcshaped, and diskshaped 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 (a /W) 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 (Kahn tear test)
The tear test (e.g. Kahn tear test) provides a semiquantitative 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 (e.g. 1100, 3003), where
linear elastic fracture mechanics do not apply (see properties in practice).
Fracture toughness of AISI steel
The fracture toughness of AISI 4340 steel has been determined by several methods, i.e. (i)Jr curve, (ii)δr
curve, (iii) Kr curve, (iv) stretch zone size measurements (v) nonlinear energy method of Poulose et al. and
by (vi) 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 (i) Hanhn and Rosenfield, (ii) Rolfe and Barsom and
(iii) 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.[8]
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. Nonlinear 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 (the Measurement of Wet and Dry
Bulb Temperatures)
E399 Test Method for Plainstrain 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 SurfaceCrack Tension Specimens
E1823 Terminology Relating to Fatigue and Fracture Testing
IEEE/ASTM SI 10 Standard for Use of the International System of Units (SI) (The Modern Metric

System)[9]
ISO 28079:2009, the Palmqvist method, used to determine the fracture toughness for cemented
carbides.[10]
Strain Energy Release Rate
For twodimensional problems (plane stress, plane strain, antiplane shear) involving cracks that move in a
straight path, the mode I stress intensity factor is related to the energy release rate, also in mode I,
by
where is the Young's modulus and for plane stress and for plane strain.
See also
Puncture resistance
Brittleductile transition zone
Charpy impact test
Impact (mechanics)
Izod impact strength test
Toughness of ceramics by indentation
Shock (mechanics)
References
1. Hertzberg, Richard W. (December 1995). Deformation and Fracture Mechanics of Engineering Materials (4
ed.). Wiley. ISBN 0471012149.
2. Sérgio Francisco dos Santos, José de Anchieta Rodrigues (2003). "Correlation Between Fracture Toughness,
Work of Fracture and Fractal Dimensions of AluminaMulliteZirconia Composites". Materials Research 6 (2):
219–226. doi:10.1590/s151614392003000200017.
3. AR Boccaccini, S Atiq, DN Boccaccini, I Dlouhy, C Kaya (2005). "Fracture behaviour of mullite fibre
reinforcedmullite matrix composites under quasistatic and ballistic impact loading". Composites Science and
Technology 65: 325–333. doi:10.1016/j.compscitech.2004.08.002.
4. J. Phalippou, T. Woignier, R. Rogier (1989). "Fracture toughness of silica aerogels". Journal de Physique
Colloques 50: C4–191. doi:10.1051/jphyscol:1989431.
5. Wei, Robert (2010), Fracture Mechanics: Integration of Mechanics, Materials Science and Chemistry,
Cambridge University Press, retrieved 24 September 2014
6. Liang, Yiling (2010), The toughening mechanism in hybrid epoxysilicarubber nanocomposites, Lehigh
University, p. 20, retrieved 24 September 2014
7. Padture, Nitin (12 April 2002). "Thermal Barrier Coatings for GasTurbine Engine Applications". Science 296:
280–284. Bibcode:2002Sci...296..280P. doi:10.1126/science.1068609.
8. Engineering Fracture Mechanics, Volume 25, Issue 4, 1986
9. NIST SRM 2100 Fracture Toughness of Ceramics
10. ISO 28079:2009, Palmqvist toughness test
(http://www.iso.org/iso/iso_catalogue/catalogue_tc/catalogue_detail.htm?csnumber=44495), Retrieved 22 January
2016

Other references
Anderson, T L., Fracture Mechanics: Fundamentals and Applications (CRC Press, Boston 1995).
Davidge, R. W., Mechanical Behavior of Ceramics (Cambridge University Press 1979).
Lawn, B., Fracture of Brittle Solids (Cambridge University Press 1993, 2nd edition).
Knott, Fundamentals of Fracture Mechanics (1973).
Foroulis (ed.), EnvironmentallySensitive Fracture of Engineering Materials (1979).
Suresh, S., Fatigue of Materials (Cambridge University Press 1998, 2nd edition).
West, J.M., Basic Corrosion & Oxidation (Horwood 1986, 2nd edn), chap.12.
Green, D.J.; Hannink, R.; Swain, M. V. (1989). Transformation Toughening of Ceramics, Boca
Raton: CRC Press. ISBN 0849365945.
http://www.sv.vt.edu/classes/MSE2094_NoteBook/97ClassProj/exper/gordon/www/fractough.html
http://www.springerlink.com/content/v2m7u4qm53172069/fulltext.pdf sriram
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