Fracture 261967 226163195 2008-07-17T02:51:54Z 124.105.86.83 /* Types of fracture */ {{otheruses}} {{Mechanical_failure_modes}} 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, 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]]. ==Types of fracture== ===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.{{Fact|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|300px|right|thumb| Schematic representation of the steps in ductile fracture.]] In ''[[ductile]] fracture'', extensive plastic deformation takes place before fracture. 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.{{Fact|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 of ductile fracture are necking (which results in stress localization at the point on the sample of smallest cross-sectional area), void formation, void coalescence (also known as crack formation), crack propagation, and failure, often resulting in a cup-and-cone shaped failure surface. <!--[[Image:ductile_fracture.PNG|right|frame| Schematic representation of the steps in ductile fracture.]]--> one of the cause of this when you fall from a height. ==Crack Separation Modes== [[Image:Fracture modes v2.svg|right|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]]. ==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]] * [[Rupture (engineering)]] * [[Structural failure]] ==Bibliography== *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] [[Category:Materials science]] [[Category:Building defects]] [[Category:Elasticity (physics)]] [[Category:Plasticity]] [[Category:Solid mechanics]] [[Category:Mechanics]] [[de:Sprödbruch]] [[es:Fractura (geología)]] [[eu:Fraktura]] [[fr:Rupture (matériau)]] [[gl:Fractura mecánica]] [[io:Rupto]] [[it:Frattura (metallurgia)]] [[lv:Plaisa]] [[nl:Breuk (mechanica)]] [[ja:断口]] [[pl:Przełam]] [[ru:Трещина]] [[fi:Haurasmurtuma]]