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A '''fracture''' is the (local) separation of an object or material into two, or more, pieces under the action of [[stress (physics)|stress]].

The word ''fracture'' is often applied to [[bone]]s of living creatures (that is, a [[bone fracture]]), or to [[crystal]]s or crystalline materials, such as [[gemstone]]s or [[metal]].  Sometimes, in crystalline materials, individual crystals fracture without the body actually separating into two or more pieces. Depending on the substance which is fractured, a fracture reduces [[strength of materials|strength]] (most substances) or inhibits [[transmission (telecommunications)|transmission]] of [[light]] ([[optical]] crystals).

A detailed understanding of how fracture occurs in materials may be assisted by the study of [[fracture mechanics]].

==Fracture strength==
[[Image:Stress v strain Aluminum 2.png|thumb|Stress vs. strain curve typical of aluminum<br>
1. [[Ultimate tensile strength]]<br>
2. [[Yield strength]]<br>
3. Proportional limit stress<br>
4. Fracture<br>
5. Offset strain (typically 0.2%)]]

'''Fracture strength''', also known as '''breaking strength''', is the stress at which a specimen fails via fracture.<ref name="degarmo">{{Citation | last = Degarmo | first = E. Paul | last2 = Black | first2 = J T. | last3 = Kohser | first3 = Ronald A. | title = Materials and Processes in Manufacturing | publisher = Wiley | page = 32 | year = 2003 | edition = 9th | isbn = 0-471-65653-4 | postscript =.}}</ref> This is usually determined for a given specimen by a [[tensile test]], which charts the [[stress-strain curve]] (see image). The final recorded point is the fracture strength.

[[Ductile]] materials have a fracture strength lower than the [[ultimate tensile strength]] (UTS), whereas in [[brittle]] materials the fracture strength is equivalent to the UTS.<ref name="degarmo"/> If a ductile material reaches its ultimate tensile strength in a load-controlled situation,{{#tag:ref|A simple load-controlled tensile situation would be to support a specimen from above, and hang a weight from the bottom end.  The load on the specimen is then independent of its deformation.|group="Note"}} it will continue to deform, with no additional load application, until it [[rupture (engineering)|ruptures]].  However, if the loading is displacement-controlled,{{#tag:ref|A simple displacement-controlled tensile situation would be to attach a very stiff [[Jack (device)|jack]] to the ends of a specimen.  As the jack extends, it controls the displacement of the specimen; the load on the specimen is dependent on the deformation.|group="Note"}} the deformation of the material may relieve the load, preventing rupture.

If the stress-strain curve is plotted in terms of ''true stress'' and ''true strain'' the curve will always slope upwards and never reverse, as true stress is corrected for the decrease in cross-sectional area.  The true stress on the material at the time of rupture is known as the breaking strength.  This is the maximum stress on the true stress-strain curve, given by point 3 on curve B.

==Types==
===Brittle fracture===<!-- This section is linked from [[Ceramic]] -->
[[Image:Glass fracture.jpg|right|thumb|250px| Brittle fracture in [[glass]].]]
[[Image:Pedalarm Bruch.jpg|right|thumb|250px|Fracture of an Aluminum Crank Arm. Bright: Brittle fracture. Dark: Fatigue fracture.]]

In ''[[brittle]] fracture'', no apparent [[plasticity (physics)|plastic deformation]] takes place before fracture.  In brittle crystalline materials, fracture can occur by ''[[cleavage (crystal)|cleavage]]'' as the result of [[tensile stress]] acting normal to crystallographic planes with low bonding (cleavage planes).  In [[amorphous solid]]s, by contrast, the lack of a crystalline structure results in a [[conchoidal fracture]], with cracks proceeding normal to the applied tension.

The theoretical strength of a crystalline material is (roughly)
:<math>\sigma_\mathrm{theoretical} = \sqrt{ \frac{E \gamma}{r_o} }</math>
where: -
:<math>E</math> is the [[Young's modulus]] of the material,
:<math>\gamma</math> is the [[surface energy]], and
:<math>r_o</math> is the equilibrium distance between atomic centers.

On the other hand, a crack introduces a stress concentration modeled by
:<math>\sigma_\mathrm{elliptical\ crack} = \sigma_\mathrm{applied}(1 + 2 \sqrt{ \frac{a}{\rho}}) = 2 \sigma_\mathrm{applied} \sqrt{\frac{a}{\rho}} </math> (For sharp cracks)
where: -
:<math>\sigma_\mathrm{applied}</math> is the loading stress,
:<math>a</math> is half the length of the crack, and
:<math>\rho</math> is the radius of curvature at the crack tip.

Putting these two equations together, we get
:<math>\sigma_\mathrm{fracture} = \sqrt{ \frac{E \gamma \rho}{4 a r_o}}.</math>

Looking closely, we can see that sharp cracks (small <math>\rho</math>) and large defects (large <math>a</math>) both lower the fracture strength of the material.

Recently, scientists have discovered [[supersonic fracture]], the phenomenon of crack motion faster than the speed of sound in a material.{{Citation needed|date=February 2007}}  This phenomenon was recently also verified by experiment of fracture in [[rubber]]-like materials.

===Ductile fracture===
[[Image:DuctileFailure.jpg|left|thumb|250px|Ductile failure of a specimen strained axially.]]
[[Image:ductile fracture upd.png|thumb|Schematic representation of the steps in ductile fracture (in pure tension).]]

In ''[[ductile]] fracture'', extensive plastic deformation ([[necking (engineering)|necking]]) takes place before fracture. The terms ''rupture'' or ''ductile rupture'' describe the [[ultimate failure]] of [[toughness|tough]] ductile materials loaded in tension. Rather than cracking, the material "pulls apart," generally leaving a rough surface. In this case there is slow propagation and an absorption of a large amount energy before fracture.{{Fact|date=February 2007}}

Many ductile metals, especially materials with high purity, can sustain very large deformation of 50–100% or more [[Strain (materials science)|strain]] before fracture under favorable loading condition and environmental condition. The strain at which the fracture happens is controlled by the purity of the materials. At room temperature, pure [[iron]] can undergo deformation up to 100% strain before breaking, while [[cast iron]] or [[plain-carbon steel|high-carbon steels]] can barely sustain 3% of strain.{{Citation needed|date=February 2007}}

Because ductile rupture involves a high degree of plastic deformation, the fracture behavior of a propagating crack as modeled above changes fundamentally. Some of the energy from stress concentrations at the crack tips is dissipated by plastic deformation before the crack actually propagates.

The basic steps are: void formation, void coalescence (also known as crack formation), crack propagation, and failure, often resulting in a cup-and-cone shaped failure surface.

==Crack separation modes==
[[Image:Fracture modes v2.svg|left|300px|thumb|The three fracture modes.]]

There are three ways of applying a force to enable a crack to propagate:<br>
*'''Mode I crack''' – Opening mode (a [[tensile stress]] normal to the plane of the crack)
*'''Mode II crack''' – Sliding mode (a [[shear stress]] acting parallel to the plane of the crack and perpendicular to the crack front)
*'''Mode III crack''' – Tearing mode (a [[shear stress]] acting parallel to the plane of the crack and parallel to the crack front)

For more information, see [[fracture mechanics]].
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==See also==
* [[Bone fracture]]
* [[Brittle-ductile transition zone]]
* [[Environmental stress fracture]]
* [[Fracture mechanics]]
* [[Fracture (mineralogy)]]
* [[Fracture (geology)]]
* [[Fracture toughness]]
* [[Fractography]]
* [[Forensic engineering]]
* [[Forensic materials engineering]]
* [[Microvoid coalescence]]
* [[Rupture (engineering)]]
* [[Structural failure]]

==Notes==
{{Reflist|group=Note}}

==References==
{{Reflist}}

==Further reading==
*Dieter, G. E. (1988) ''Mechanical Metallurgy'' ISBN 0-07-100406-8
* A. Garcimartin, A. [[Alessio Guarino|Guarino]], L. Bellon and S. Cilberto (1997) " Statistical Properties of Fracture Precursors ". Physical Review Letters, 79, 3202 (1997)
* Callister, Jr., William D. (2002) ''Materials Science and Engineering: An Introduction.'' ISBN 0-471-13576-3
* Peter Rhys Lewis, Colin Gagg, Ken Reynolds, CRC Press (2004), ''Forensic Materials Engineering: Case Studies''.

==External links==
* Web postings at http://www.jwave.vt.edu/crcd/farkas/lectures/Fract1/tsld006.htm
* Virtual museum of failed products at http://materials.open.ac.uk/mem/index.html
*[http://videophysics.com/fracture.htm Fracture and Reconstruction of a Clay Bowl]
*[http://www.msm.cam.ac.uk/phase-trans/2008/weld/weld.html Ductile fracture]
*[http://www.sv.vt.edu/classes/MSE2094_NoteBook/97ClassProj/exper/halahan/www/halahan.html Modes of Fracture from Virginia Tech Materials Science and Engineering]


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[[Category:Anatomy]]
[[Category:Pathology]]

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