Fracture

A fracture is the separation of an object or material into two or more pieces under the action of 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.[1] Fracture strength or breaking strength is the stress when a specimen fails or fractures.

The word fracture is often applied to bones of living creatures (i.e. a bone fracture), or to crystalline materials, such as gemstones or metal. Sometimes, individual crystals fracture without the structure actually separating into two or more pieces. Depending on the substance, a fracture reduces strength (most substances) or inhibits transmission of waves, such as light (optical crystals). A detailed understanding of how fracture occurs in materials may be assisted by the study of fracture mechanics.

Fracture strength

Stress vs. strain curve typical of aluminum
1. Ultimate tensile strength
2. Yield strength
3. Proportional limit stress
4. Fracture
5. Offset strain (typically 0.2%)

Fracture strength, also known as breaking strength, is the stress at which a specimen fails via fracture.[2] 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.[2] If a ductile material reaches its ultimate tensile strength in a load-controlled situation,[Note 1] it will continue to deform, with no additional load application, until it ruptures. However, if the loading is displacement-controlled,[Note 2] the deformation of the material may relieve the load, preventing rupture.

Types

Brittle fracture

Brittle fracture in glass
Fracture of an aluminum crank arm of a bicycle, where Bright= brittle fracture, Dark= fatigue fracture.

In brittle fracture, no apparent plastic deformation takes place before fracture. In brittle crystalline materials, fracture can occur by cleavage as the result of tensile stress acting normal to crystallographic planes with low bonding (cleavage planes). In amorphous solids, by contrast, the lack of a crystalline structure results in a conchoidal fracture, with cracks proceeding normal to the applied tension. The sinking of RMS Titanic in 1912 from an iceberg collision is widely reported to have been due to brittle fracture of the hull's steel plates.[3]

The theoretical strength of a crystalline material is (roughly)

where: -

is the Young's modulus of the material,
is the surface energy, and
is the equilibrium distance between atomic centers.

On the other hand, a crack introduces a stress concentration modeled by

(For sharp cracks)

where: -

is the loading stress,
is half the length of the crack, and
is the radius of curvature at the crack tip.

Putting these two equations together, we get

Looking closely, we can see that sharp cracks (small ) and large defects (large ) 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.[4] This phenomenon was recently also verified by experiment of fracture in rubber-like materials.

Brittle fracture may be avoided by limiting pressure and temperature within limits. Each system has a brittle fracture prevention limit curve defined by the weakest components at given temperatures and pressures allowing for the largest undetected preexisting flaw in each component.

Ductile fracture

Ductile failure of a specimen strained axially

In ductile fracture, extensive plastic deformation (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 energy before fracture. The ductility of a material is also referred to as toughness.

Schematic representation of the steps in ductile fracture (in pure tension)

Many ductile metals, especially materials with high purity, can sustain very large deformation of 50–100% or more 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 high-carbon steels can barely sustain 3% of strain.

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.

Crack separation modes

There are three ways of applying a force to enable a crack to propagate:

Fracture crack separation modes

Crack initiation and propagation accompany fracture. The manner by which the crack propagates through the material gives great insight into the mode of fracture. In ductile materials (ductile fracture), the crack moves slowly and is accompanied by a large amount of plastic deformation around the crack tip. The crack will usually not extend unless an increased stress is applied. On the other hand, in dealing 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 and increase in magnitude once they are initiated. In a part made of a ductile material, the crack may progress to a section of the part where stresses a slighly lower and stop due to the blunting effect of plastic deformations at the crack tip. Another important mannerism of crack propagation is the way in which the advancing crack travels through the material. A crack that passes through the grains within the material is undergoing transgranular fracture. However, a crack that propagates along the grain boundaries is termed an intergranular fracture.

See also

Notes

  1. ↑ 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.
  2. ↑ A simple displacement-controlled tensile situation would be to attach a very stiff 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.

References

  1. ↑ Cherepanov, G.P., Mechanics of Brittle Fracture
  2. 1 2 Degarmo, E. Paul; Black, J T.; Kohser, Ronald A. (2003), Materials and Processes in Manufacturing (9th ed.), Wiley, p. 32, ISBN 0-471-65653-4.
  3. ↑
  4. ↑ C. H. Chen; H. P. Zhang; J. Niemczura; K. Ravi-Chandar; M. Marder (November 2011). "Scaling of crack propagation in rubber sheets". Europhysics Letters. 96 (3): 36009. Bibcode:2011EL.....9636009C. doi:10.1209/0295-5075/96/36009.

Further reading

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