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{{about|fractures in general|bone fractures|Bone fracture|other uses|Fracture (disambiguation)}}
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{{Mechanical failure modes}}

A '''fracture''' is the separation of an object or material into two or more pieces under the action of [[stress (physics)|stress]]. The fracture of a solid usually occurs due to the development of certain displacement discontinuity surfaces within the solid. If a displacement develops perpendicular to the surface of displacement, it is called a normal tensile crack or simply a crack; if a displacement develops tangentially to the surface of displacement, it is called a shear crack, slip band, or dislocation.<ref name="cherepanov">{{Citation |last= Cherepanov |first= G.P. |title= Mechanics of Brittle Fracture}}</ref>

Brittle fractures occur with no apparent deformation before fracture; ductile fractures occur when visible deformation does occur before separation.  '''Fracture strength''' or '''breaking strength''' is the stress when a specimen fails or fractures.  A detailed understanding of how fracture occurs in materials may be assisted by the study of [[fracture mechanics]].

==Fracture strength==
[[File: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 [[Structural integrity and failure|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 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.

==Types== 
There are two types of fractures :
===Brittle fracture===<!-- This section is linked from [[Ceramic]] -->
[[File:Glass fracture.jpg|thumb|right|Brittle fracture in glass]]
[[File:Pedalarm Bruch.jpg|thumb|right|Fracture of an aluminum [[crank arm]] of a bicycle, where Bright= brittle fracture, Dark= fatigue fracture.]]

In ''[[brittleness|brittle]] fracture'', no apparent [[plasticity (physics)|plastic deformation]] takes place before fracture. Brittle fracture typically involves little energy absorption and occurs at high speeds—up to 2133.6&nbsp;m/s (7000&nbsp;ft/s) in steel.<ref name="Rolfe" /> In most cases brittle fracture will continue even when loading is discontinued.<ref name="Campbell" />

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}\left(1 + 2 \sqrt{ \frac{a}{\rho}}\right)= 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 propagation faster than the speed of sound in a material.<ref>{{cite journal |author1=C. H. Chen |author2=H. P. Zhang |author3=J. Niemczura |author4=K. Ravi-Chandar |author5=M. Marder |title=Scaling of crack propagation in rubber sheets |journal=Europhysics Letters |volume=96 |issue=3|pages=36009 |date=November 2011 |doi=10.1209/0295-5075/96/36009 |url=http://iopscience.iop.org/0295-5075/96/3/36009/|bibcode= 2011EL.....9636009C }}</ref> This phenomenon was recently also verified by experiment of fracture in rubber-like materials.

The basic sequence in a typical brittle fracture is: introduction of a flaw either before or after the material is put in service, slow and stable crack propagation under recurring loading, and sudden rapid failure when the crack reaches critical crack length based on the conditions defined by fracture mechanics.<ref name="Campbell">{{cite book|last1=Campbell|first1=edited by F.C.|title=Fatigue and fracture : understanding the basics|date=2012|publisher=ASM International|location=Materials Park, Ohio|isbn=1615039767}}</ref> Brittle fracture may be avoided by controlling three primary factors: material [[fracture toughness]] (K<sub>c</sub>), nominal stress level (σ), and introduced flaw size (a).<ref name="Rolfe">{{cite book|last1=Rolfe|first1=John M. Barsom, Stanley T.|title=Fracture and fatigue control in structures : applications of fracture mechanics|date=1999|publisher=ASTM|location=West Conshohocken, Pa.|isbn=0803120826|edition=3.}}</ref> Residual stresses, temperature, loading rate, and stress concentrations also contribute to brittle fracture by influencing the three primary factors.<ref name="Rolfe" />

Under certain conditions, ductile materials can exhibit brittle behavior. Rapid loading, low temperature, and triaxial stress constraint conditions may cause ductile materials to fail without prior deformation.<ref name="Rolfe" />

===Ductile fracture===
[[File:DuctileFailure.jpg|left|thumb|Ductile failure of a specimen strained axially]]

In ''[[ductility|ductile]] fracture'', extensive plastic deformation ([[necking (engineering)|necking]]) takes place before fracture. The terms ''rupture'' or ''ductile rupture'' describe the [[ultimate failure]] of 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 of energy before fracture.<ref>{{cite book|last1=Perez|first1=Nestor|title=Fracture Mechanics|date=2016|publisher=Springer|isbn=3319249975|edition=2nd}}</ref>

[[File:ductile fracture upd.png|thumb|Schematic representation of the steps in ductile fracture (in pure tension)]]

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

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

== Fracture modes and characteristics ==
{{main|Fracture mechanics}}

There are three standard conventions for defining relative displacements in elastic materials in order to analyze crack propagation<ref name="Rolfe" /> as proposed by [[George Rankine Irwin|Irwin]].<ref name="Jin">{{cite book|last1=Jin|first1=C.T. Sun, Z.-H.|title=Fracture mechanics|date=2012|publisher=Academic Press|location=Waltham, MA|isbn=9780123850010}}</ref> In addition fracture can involve uniform strain or a combination of these modes.<ref name="Campbell" />
[[File:Fracture modes v2.svg|thumb|left|Fracture crack separation modes]]
*'''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)

The manner in which a crack propagates through a material gives insight into the mode of fracture. With ductile fracture a crack moves slowly and is accompanied by a large amount of plastic deformation around the crack tip. A ductile crack will usually not propagate unless an increased stress is applied and generally cease propagating when loading is removed.<ref name="Campbell" /> In a ductile material, a crack may progress to a section of the material where stresses are slightly lower and stop due to the blunting effect of plastic deformations at the crack tip. On the other hand, with brittle fracture, cracks spread very rapidly with little or no plastic deformation. The cracks that propagate in a brittle material will continue to grow once initiated.

Crack propagation is also categorized by the crack characteristics at the microscopic level. A crack that passes through the grains within the material is undergoing transgranular fracture. A crack that propagates along the grain boundaries is termed an intergranular fracture.  Typically, the bonds between material grains are stronger at room temperature than the material itself, so transgranular fracture is more likely to occur. When temperatures increase enough to weaken the grain bonds, intergranular fracture is the more common fracture mode.<ref name="Campbell" />

==Fracture Testing==
Fracture in materials is studied and quantified in multiple ways. Fracture is largely determined by the fracture toughness (<math display="inline">\mathrm{K}_\mathrm{c}</math>), so fracture testing is often done to determine this. The two most widely-used techniques for determining fracture toughness are the [[Three-point flexural test]] and the [[Compact tension specimen|compact tension test]]. 

By performing the compact tension and three-point flexural tests, one is able to determine the fracture toughness through the following equation: 

:<math>\mathrm{K_{c}} = \sigma_\mathrm{F}\sqrt{\pi \mathrm{c}}\mathrm{f \ (c/a)}</math>

Where:-
:<math>\mathrm{f \ (c/a)}</math> is an empirically-derived equation to capture the test sample geometry
:<math>\sigma_\mathrm{F}</math> is the fracture stress, and 
:<math>\mathrm{c}</math> is the crack length.

To accurately attain <math display="inline">\mathrm{K}_\mathrm{c}</math>, the value of <math display="inline">\mathrm{c}</math> must be precisely measured. This is done by taking the test piece with its fabricated [[Notch_(engineering)| notch]] of length <math display="inline">\mathrm{c\prime}</math> and sharpening this [[Notch_(engineering)| notch]] to better emulate a crack tip found in real-world materials  <ref name=efm>[https://hal.archives-ouvertes.fr/hal-02310717 EFM - Stress concentration at notches] a closer look </ref>. Cyclical prestressing the sample can then induce a fatigue crack which extends the crack from the fabricated notch length of <math display="inline">\mathrm{c\prime}</math>  to <math display="inline">\mathrm{c}</math>. This value <math display="inline">\mathrm{c}</math> is used in the above equations for determining <math display="inline">\mathrm{K}_\mathrm{c}</math>.<ref name="Courtney">{{Citation |last= Courtney |first= Thomas H.|title= Mechanical behavior of materials |publisher= McGraw Hill |year= 2000 |edition= 3nd |isbn= 1-57766-425-6 |postscript =.}}</ref>

Following this test, the sample can then be reoriented such that further loading of a load (F) will extend this crack and thus a load versus sample deflection curve can be obtained. With this curve, the slope of the linear portion, which is the inverse of the compliance of the material, can be obtained. This is then used to derive f(c/a) as defined above in the equation. With the knowledge of all these variables, <math display="inline">\mathrm{K}_\mathrm{c}</math> can then be calculated.

==Brittle Fracture of Ceramics and Inorganic Glasses==
Ceramics and inorganic glasses have fracturing behavior that differ those of metallic materials. Ceramics have high strengths and perform well in high temperatures due to the material strength being independent of temperature. Ceramics have low toughness as determined by testing under a tensile load; often, ceramics have <math display="inline">\mathrm{K}_\mathrm{c}</math> values that are ~5% of that found in metals.<ref name="Courtney" /> However, ceramics are usually loaded in compression in everyday use, so the compressive strength is often referred to as the strength; this strength can often exceed that of most metals. However, ceramics are brittle and thus most work done revolves around preventing brittle fracture. Due to how ceramics are manufactured and processed, there are often preexisting defects in the material introduce a high degree of variability in the Mode I brittle fracture.<ref name="Courtney" /> Thus, there is a probabilistic nature to be accounted for in the design of ceramics. The [[Weibull distribution]] predicts the survival probability of a fraction of samples with a certain volume that survive a tensile stress sigma, and is often used to better assess the success of a ceramic in avoiding fracture.

==Notable fracture failures==
Failures caused by brittle fracture have not been limited to any particular category of engineered structure.<ref name="Rolfe"/> Though brittle fracture is less common than other types of failure, the impacts to life and property can be more severe.<ref name="Rolfe" /> The following notable historic failures were attributed to brittle fracture:
*Pressure vessels: [[Great Molasses Flood#Causes|Great Molasses Flood]] in 1919,<ref name="Rolfe" /> New Jersey molasses tank failure in 1973<ref name="Campbell"/> 
*Bridges: [[King Street Bridge (Melbourne)|King Street Bridge]] span collapse in 1962, [[Silver Bridge#Wreckage analysis|Silver Bridge]] collapse in 1967,<ref name="Rolfe" /> partial failure of the [https://www.fhwa.dot.gov/bridge/steel/010710.cfm Hoan Bridge] in 2000 
*Ships: [[RMS Titanic#Building and preparing the ship|Titanic]] in 1912,<ref name="Campbell" /> [[Liberty ship#Problems|Liberty ships]] during World War II,<ref name="Rolfe" /> [[SS Schenectady]] in 1943<ref name="Campbell" />

==See also==
* [[Environmental stress fracture]]
* [[Fracture (mineralogy)]]
* [[Notch_(engineering)| Notch]]
* [[Fracture (geology)]]
* [[Fractography]]
* [[Forensic engineering]]
* [[Forensic materials engineering]]
* [[Gilbert tessellation]]
* [[Microvoid coalescence]]

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

==References==
{{Reflist}}

==Further reading==
* Alireza Bagher Shemirani, Haeri, H., Sarfarazi,V., Hedayat, A., ''A review paper about experimental investigations on failure behaviour of non-persistent joint''.Geomechanics and Engineering, Vol. 13, No. 4, (2017), 535–570, [http://doi.org/10.12989/gae.2017.13.4.535] 
* 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==
* 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]

{{Patterns in nature}}
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[[Category:Materials science]]
[[Category:Building defects]]
[[Category:Elasticity (physics)]]
[[Category:Plasticity (physics)]]
[[Category:Solid mechanics]]
[[Category:Fracture mechanics]]
[[Category:Mechanics]]
[[Category:Glass physics]]