Fracture

Fracture

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A fracture is the separation of an object or material into two, or more, pieces under the action of stress
Stress (physics)
In continuum mechanics, stress is a measure of the internal forces acting within a deformable body. Quantitatively, it is a measure of the average force per unit area of a surface within the body on which internal forces act. These internal forces are a reaction to external forces applied on the body...

.

The word fracture is often applied to bone
Bone
Bones are rigid organs that constitute part of the endoskeleton of vertebrates. They support, and protect the various organs of the body, produce red and white blood cells and store minerals. Bone tissue is a type of dense connective tissue...

s of living creatures (that is, a bone fracture
Bone fracture
A bone fracture is a medical condition in which there is a break in the continuity of the bone...

), or to crystal
Crystal
A crystal or crystalline solid is a solid material whose constituent atoms, molecules, or ions are arranged in an orderly repeating pattern extending in all three spatial dimensions. The scientific study of crystals and crystal formation is known as crystallography...

s or crystalline materials, such as gemstone
Gemstone
A gemstone or gem is a piece of mineral, which, in cut and polished form, is used to make jewelry or other adornments...

s or metal
Metal
A metal , is an element, compound, or alloy that is a good conductor of both electricity and heat. Metals are usually malleable and shiny, that is they reflect most of incident light...

. 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
Strength of materials
In materials science, the strength of a material is its ability to withstand an applied stress without failure. The applied stress may be tensile, compressive, or shear. Strength of materials is a subject which deals with loads, deformations and the forces acting on a material. A load applied to a...

 (most substances) or inhibits transmission
Transmission (telecommunications)
Transmission, in telecommunications, is the process of sending, propagating and receiving an analogue or digital information signal over a physical point-to-point or point-to-multipoint transmission medium, either wired, optical fiber or wireless...

 of light
Light
Light or visible light is electromagnetic radiation that is visible to the human eye, and is responsible for the sense of sight. Visible light has wavelength in a range from about 380 nanometres to about 740 nm, with a frequency range of about 405 THz to 790 THz...

 (optical crystals).

A detailed understanding of how fracture occurs in materials may be assisted by the study of fracture mechanics
Fracture mechanics
Fracture mechanics is the field of mechanics concerned with the study of the propagation of cracks in materials. It uses methods of analytical solid mechanics to calculate the driving force on a crack and those of experimental solid mechanics to characterize the material's resistance to fracture.In...

.

Fracture strength


Fracture strength, also known as breaking strength, is the stress at which a specimen fails via fracture. This is usually determined for a given specimen by a tensile test, which charts the stress-strain curve
Stress-strain curve
During tensile testing of a material sample, the stress–strain curve is a graphical representation of the relationship between stress, derived from measuring the load applied on the sample, and strain, derived from measuring the deformation of the sample, i.e. elongation, compression, or distortion...

 (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
Brittle
A material is brittle if, when subjected to stress, it breaks without significant deformation . Brittle materials absorb relatively little energy prior to fracture, even those of high strength. Breaking is often accompanied by a snapping sound. Brittle materials include most ceramics and glasses ...

 materials the fracture strength is equivalent to the UTS. If a ductile material reaches its ultimate tensile strength in a load-controlled situation, it will continue to deform, with no additional load application, until it ruptures. However, if the loading is displacement-controlled, 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.

Brittle fracture



In brittle
Brittle
A material is brittle if, when subjected to stress, it breaks without significant deformation . Brittle materials absorb relatively little energy prior to fracture, even those of high strength. Breaking is often accompanied by a snapping sound. Brittle materials include most ceramics and glasses ...

 fracture
, no apparent plastic deformation
Plasticity (physics)
In physics and materials science, plasticity describes the deformation of a material undergoing non-reversible changes of shape in response to applied forces. For example, a solid piece of metal being bent or pounded into a new shape displays plasticity as permanent changes occur within the...

 takes place before fracture. In brittle crystalline materials, fracture can occur by cleavage
Cleavage (crystal)
Cleavage, in mineralogy, is the tendency of crystalline materials to split along definite crystallographic structural planes. These planes of relative weakness are a result of the regular locations of atoms and ions in the crystal, which create smooth repeating surfaces that are visible both in the...

as the result of tensile stress acting normal to crystallographic planes with low bonding (cleavage planes). In amorphous solid
Amorphous solid
In condensed matter physics, an amorphous or non-crystalline solid is a solid that lacks the long-range order characteristic of a crystal....

s, by contrast, the lack of a crystalline structure results in a conchoidal fracture
Conchoidal fracture
Conchoidal fracture describes the way that brittle materials break when they do not follow any natural planes of separation. Materials that break in this way include flint and other fine-grained minerals, as well as most amorphous solids, such as obsidian and other types of glass.Conchoidal...

, with cracks proceeding normal to the applied tension.

The theoretical strength of a crystalline material is (roughly)
where: - is the Young's modulus
Young's modulus
Young's modulus is a measure of the stiffness of an elastic material and is a quantity used to characterize materials. It is defined as the ratio of the uniaxial stress over the uniaxial strain in the range of stress in which Hooke's Law holds. In solid mechanics, the slope of the stress-strain...

 of the material, is the surface energy
Surface energy
Surface energy quantifies the disruption of intermolecular bonds that occur when a surface is created. In the physics of solids, surfaces must be intrinsically less energetically favorable than the bulk of a material, otherwise there would be a driving force for surfaces to be created, removing...

, 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
Supersonic fracture
Supersonic fractures are fractures where the fracture velocity moves faster than the speed of sound in the material. This phenomenon was first discovered by scientists from the Max Planck Institute for Metals Research in Stuttgart and IBM Almaden Research Center in San Jose, California Supersonic...

, the phenomenon of crack motion faster than the speed of sound in a material. This phenomenon was recently also verified by experiment of fracture in rubber
Rubber
Natural rubber, also called India rubber or caoutchouc, is an elastomer that was originally derived from latex, a milky colloid produced by some plants. The plants would be ‘tapped’, that is, an incision made into the bark of the tree and the sticky, milk colored latex sap collected and refined...

-like materials.

Ductile fracture



In ductile fracture, extensive plastic deformation (necking
Necking (engineering)
Necking, in engineering or materials science, is a mode of tensile deformation where relatively large amounts of strain localize disproportionately in a small region of the material. The resulting prominent decrease in local cross-sectional area provides the basis for the name "neck"...

) takes place before fracture. The terms rupture or ductile rupture describe the ultimate failure
Ultimate failure
In mechanical engineering, ultimate failure describes the breaking of a material. In general there are two types of failure: fracture and buckling. Fracture of a material occurs when either an internal or external crack elongates the width or length of the material. In ultimate failure this will...

 of tough
Toughness
In materials science and metallurgy, toughness is the ability of a material to absorb energy and plastically deform without fracturing; Material toughness is defined as the amount of energy per volume that a material can absorb before rupturing...

 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.

Many ductile metals, especially materials with high purity, can sustain very large deformation of 50–100% or more strain
Strain (materials science)
In continuum mechanics, the infinitesimal strain theory, sometimes called small deformation theory, small displacement theory, or small displacement-gradient theory, deals with infinitesimal deformations of a continuum body...

 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
Iron
Iron is a chemical element with the symbol Fe and atomic number 26. It is a metal in the first transition series. It is the most common element forming the planet Earth as a whole, forming much of Earth's outer and inner core. It is the fourth most common element in the Earth's crust...

 can undergo deformation up to 100% strain before breaking, while cast iron
Cast iron
Cast iron is derived from pig iron, and while it usually refers to gray iron, it also identifies a large group of ferrous alloys which solidify with a eutectic. The color of a fractured surface can be used to identify an alloy. White cast iron is named after its white surface when fractured, due...

 or high-carbon steels
Plain-carbon steel
Carbon steel, also called plain-carbon steel, is steel where the main interstitial alloying constituent is carbon. The American Iron and Steel Institute defines carbon steel as: "Steel is considered to be carbon steel when no minimum content is specified or required for chromium, cobalt,...

 can barely sustain 3% of strain.

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


There are three ways of applying a force to enable a crack to propagate:
  • Mode I crack – Opening mode (a tensile stress normal to the plane of the crack)
  • Mode II crack – Sliding mode (a shear stress
    Shear stress
    A shear stress, denoted \tau\, , is defined as the component of stress coplanar with a material cross section. Shear stress arises from the force vector component parallel to the cross section...

     acting parallel to the plane of the crack and perpendicular to the crack front)
  • Mode III crack – Tearing mode (a shear stress
    Shear stress
    A shear stress, denoted \tau\, , is defined as the component of stress coplanar with a material cross section. Shear stress arises from the force vector component parallel to the cross section...

     acting parallel to the plane of the crack and parallel to the crack front)


For more information, see fracture mechanics
Fracture mechanics
Fracture mechanics is the field of mechanics concerned with the study of the propagation of cracks in materials. It uses methods of analytical solid mechanics to calculate the driving force on a crack and those of experimental solid mechanics to characterize the material's resistance to fracture.In...

.

Crack initiation and propagation accompany fracture. The manner through 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. 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. 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

  • Bone fracture
    Bone fracture
    A bone fracture is a medical condition in which there is a break in the continuity of the bone...

  • Brittle-ductile transition zone
    Brittle-ductile transition zone
    The brittle-ductile transition zone is the strongest part of the Earth's crust. For quartz and feldspar rich rocks in continental crust this occurs at an approximate depth of 13–18 km . At this depth rock becomes less likely to fracture, and more likely to deform ductilely by creep...

  • Environmental stress fracture
    Environmental stress fracture
    In materials science, environmental stress fracture or environment assisted fracture is the generic name given to premature failure under the influence of tensile stresses and harmful environments of materials such as metals and alloys, composites, plastics and ceramics.Metals and alloys exhibit...

  • Fracture mechanics
    Fracture mechanics
    Fracture mechanics is the field of mechanics concerned with the study of the propagation of cracks in materials. It uses methods of analytical solid mechanics to calculate the driving force on a crack and those of experimental solid mechanics to characterize the material's resistance to fracture.In...

  • Fracture (mineralogy)
    Fracture (mineralogy)
    In the field of mineralogy, fracture is a term used to describe the shape and texture of the surface formed when a mineral is fractured. Minerals often have a highly distinctive fracture, making it a principal feature used in their identification....

  • Fracture (geology)
  • Fracture toughness
    Fracture toughness
    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 virtually all design applications. The fracture toughness of a material is determined from the...

  • Fractography
    Fractography
    Fractography is the study of fracture surfaces of materials. Fractographic methods are routinely used to determine the cause of failure in engineering structures, especially in product failure and the practice of forensic engineering or failure analysis...

  • Forensic engineering
    Forensic engineering
    Forensic engineering is the investigation of materials, products, structures or components that fail or do not operate or function as intended, causing personal injury or damage to property. The consequences of failure are dealt with by the law of product liability. The field also deals with...

  • Forensic materials engineering
    Forensic materials engineering
    A branch of Forensic engineering, the subject focuses on the material evidence from crime or accident scenes, seeking defects in those materials which might explain why an accident occurred, or the source of a specific material to identify a criminal...

  • Microvoid coalescence
    Microvoid coalescence
    Microvoid coalescence is a high energy microscopic fracture mechanism observed in the majority of metallic alloys and in some engineering plastics.-Fracture process:...

  • Rupture (engineering)
  • Structural failure
    Structural failure
    Structural failure refers to loss of the load-carrying capacity of a component or member within a structure or of the structure itself. Structural failure is initiated when the material is stressed to its strength limit, thus causing fracture or excessive deformations...


Further reading

  • Dieter, G. E. (1988) Mechanical Metallurgy ISBN 0-07-100406-8
  • A. Garcimartin, A. Guarino
    Alessio Guarino
    - Overview :Guarino works in the domain of nonlinear physics, such as liquid crystals, fracture, convection and granular matter. Sergio Ciliberto, Riccardo Scorretti and Guarino introduced a numerical technique studying the effect of thermal fluctuations in heterogeneous systems. He is currently...

    , 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