Rupture (engineering)
   HOME

TheInfoList



OR:

Fracture is the separation of an object or material into two or more pieces under the action of
stress Stress may refer to: Science and medicine * Stress (biology), an organism's response to a stressor such as an environmental condition * Stress (linguistics), relative emphasis or prominence given to a syllable in a word, or to a word in a phrase ...
. 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, it is called a normal tensile crack or simply a crack; if a displacement develops tangentially, it is called a shear crack, slip band or
dislocation In materials science, a dislocation or Taylor's dislocation is a linear crystallographic defect or irregularity within a crystal structure that contains an abrupt change in the arrangement of atoms. The movement of dislocations allow atoms to sl ...
. Brittle fractures occur with no apparent deformation before fracture. Ductile fractures occur after visible deformation. Fracture strength, or breaking strength, is the stress when a specimen fails or fractures. The detailed understanding of how a fracture occurs and develops in materials is the object of fracture mechanics.


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 Tensile testing, also known as tension testing, is a fundamental materials science and engineering test in which a sample is subjected to a controlled tension until failure. Properties that are directly measured via a tensile test are ultimat ...
, which charts the
stress–strain curve In engineering and materials science, a stress–strain curve for a material gives the relationship between stress and strain. It is obtained by gradually applying load to a test coupon and measuring the deformation, from which the stress and ...
(see image). The final recorded point is the fracture strength. Ductile materials have a fracture strength lower than the
ultimate tensile strength Ultimate tensile strength (UTS), often shortened to tensile strength (TS), ultimate strength, or F_\text within equations, is the maximum stress that a material can withstand while being stretched or pulled before breaking. In brittle materials t ...
(UTS), whereas in brittle 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. The statistics of fracture in random materials have very intriguing behavior, and was noted by the architects and engineers quite early. Indeed, fracture or breakdown studies might be the oldest physical science studies, which still remain intriguing and very much alive.
Leonardo da Vinci Leonardo di ser Piero da Vinci (15 April 14522 May 1519) was an Italian polymath of the High Renaissance who was active as a painter, Drawing, draughtsman, engineer, scientist, theorist, sculptor, and architect. While his fame initially res ...
, more than 500 years ago, observed that the tensile strengths of nominally identical specimens of iron wire decrease with increasing length of the wires (see e.g., for a recent discussion). Similar observations were made by
Galileo Galilei Galileo di Vincenzo Bonaiuti de' Galilei (15 February 1564 – 8 January 1642) was an Italian astronomer, physicist and engineer, sometimes described as a polymath. Commonly referred to as Galileo, his name was pronounced (, ). He was ...
more than 400 years ago. This is the manifestation of the extreme statistics of failure (bigger sample volume can have larger defects due to cumulative fluctuations where failures nucleate and induce lower strength of the sample). Text was copied from this source, which is available under
Creative Commons Attribution 4.0 International License


Types

There are two types of fractures: brittle and ductile fractures respectively without or with
plastic deformation In engineering, deformation refers to the change in size or shape of an object. ''Displacements'' are the ''absolute'' change in position of a point on the object. Deflection is the relative change in external displacements on an object. Strain ...
prior to failure.


Brittle

In
brittle A material is brittle if, when subjected to stress, it fractures with little elastic deformation and without significant plastic deformation. Brittle materials absorb relatively little energy prior to fracture, even those of high strength. Bre ...
fracture, no apparent
plastic deformation In engineering, deformation refers to the change in size or shape of an object. ''Displacements'' are the ''absolute'' change in position of a point on the object. Deflection is the relative change in external displacements on an object. Strain ...
takes place before fracture. Brittle fracture typically involves little energy absorption and occurs at high speeds—up to in steel. In most cases brittle fracture will continue even when loading is discontinued. In brittle crystalline materials, fracture can occur by '' cleavage'' as the result of
tensile stress In continuum mechanics, stress is a physical quantity. It is a quantity that describes the magnitude of forces that cause deformation. Stress is defined as ''force per unit area''. When an object is pulled apart by a force it will cause elonga ...
acting normal to crystallographic planes with low bonding (cleavage planes). In
amorphous solid In condensed matter physics and materials science, an amorphous solid (or non-crystalline solid, glassy solid) is a solid that lacks the long-range order that is characteristic of a crystal. Etymology The term comes from the Greek ''a'' ("wit ...
s, by contrast, the lack of a crystalline structure results in a conchoidal fracture, with cracks proceeding normal to the applied tension. The fracture strength (or micro-crack nucleation stress) of a material was first theoretically estimated by
Alan Arnold Griffith Alan Arnold Griffith (13 June 1893 – 13 October 1963), son of Victorian science fiction writer George Griffith, was an English engineer. Among many other contributions he is best known for his work on stress and fracture in metals that is no ...
in 1921: :\sigma_\mathrm= \sqrt where: – :E is the
Young's modulus Young's modulus E, the Young modulus, or the modulus of elasticity in tension or compression (i.e., negative tension), is a mechanical property that measures the tensile or compressive stiffness of a solid material when the force is applied leng ...
of the material, :\gamma is the surface energy, and :r_o is the micro-crack length (or equilibrium distance between atomic centers in a crystalline solid). On the other hand, a crack introduces a stress concentration modeled by :\sigma_\mathrm= \sigma_\mathrm\left(1 + 2 \sqrt\right)= 2 \sigma_\mathrm \sqrt (For sharp cracks) where: – :\sigma_\mathrm is the loading stress, :a is half the length of the crack, and :\rho is the radius of curvature at the crack tip. Putting these two equations together gets :\sigma_\mathrm= \sqrt. Sharp cracks (small \rho) and large defects (large a) 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. 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. Brittle fracture may be avoided by controlling three primary factors: material
fracture toughness In materials science, fracture toughness is the critical stress intensity factor of a sharp crack where propagation of the crack suddenly becomes rapid and unlimited. A component's thickness affects the constraint conditions at the tip of a c ...
(K), nominal stress level (σ), and introduced flaw size (a). Residual stresses, temperature, loading rate, and stress concentrations also contribute to brittle fracture by influencing the three primary factors. 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.


Ductile

In
ductile Ductility is a mechanical property commonly described as a material's amenability to drawing (e.g. into wire). In materials science, ductility is defined by the degree to which a material can sustain plastic deformation under tensile stres ...
fracture, extensive plastic deformation ( necking) takes place before fracture. The terms "rupture" and "ductile rupture" describe the
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 len ...
of ductile materials loaded in tension. The extensive plasticity causes the crack to propagate slowly due to the absorption of a large amount of energy before fracture. 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. Voids typically coalesce around precipitates, secondary phases, inclusions, and at grain boundaries in the material. Ductile fracture is typically transgranular and deformation due to
dislocation In materials science, a dislocation or Taylor's dislocation is a linear crystallographic defect or irregularity within a crystal structure that contains an abrupt change in the arrangement of atoms. The movement of dislocations allow atoms to sl ...
slip can cause the shear lip characteristic of cup and cone fracture.


Characteristics

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. 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.


Testing

Fracture in materials is studied and quantified in multiple ways. Fracture is largely determined by the fracture toughness (\mathrm_\mathrm), 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 The three-point bending flexural test provides values for the modulus of elasticity in bending E_f, flexural stress \sigma_f, flexural strain \epsilon_f and the flexural stress–strain response of the material. This test is performed on a uni ...
and the 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: :\mathrm = \sigma_\mathrm\sqrt\mathrm Where:- :\mathrm is an empirically-derived equation to capture the test sample geometry :\sigma_\mathrm is the fracture stress, and :\mathrm is the crack length. To accurately attain \mathrm_\mathrm, the value of \mathrm must be precisely measured. This is done by taking the test piece with its fabricated notch of length \mathrm and sharpening this notch to better emulate a crack tip found in real-world materials.EFM - Stress concentration at notches
a closer look
Cyclical prestressing the sample can then induce a
fatigue crack In materials science, fatigue is the initiation and propagation of cracks in a material due to cyclic loading. Once a fatigue crack has initiated, it grows a small amount with each loading cycle, typically producing striations on some parts of ...
which extends the crack from the fabricated notch length of \mathrm to \mathrm. This value \mathrm is used in the above equations for determining \mathrm_\mathrm. 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, \mathrm_\mathrm can then be calculated.


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 \mathrm_\mathrm values that are ~5% of that found in metals. 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. Thus, there is a probabilistic nature to be accounted for in the design of ceramics. The
Weibull distribution In probability theory and statistics, the Weibull distribution is a continuous probability distribution. It is named after Swedish mathematician Waloddi Weibull, who described it in detail in 1951, although it was first identified by Maurice Re ...
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.


Fiber bundles

To model fracture of a bundle of fibers, the Fiber Bundle Model was introduced by Thomas Pierce in 1926 as a model to understand the strength of composite materials. The bundle consists of a large number of parallel Hookean springs of identical length and each having identical spring constants. They have however different breaking stresses. All these springs are suspended from a rigid horizontal platform. The load is attached to a horizontal platform, connected to the lower ends of the springs. When this lower platform is absolutely rigid, the load at any point of time is shared equally (irrespective of how many fibers or springs have broken and where) by all the surviving fibers. This mode of load-sharing is called Equal-Load-Sharing mode. The lower platform can also be assumed to have finite rigidity, so that local deformation of the platform occurs wherever springs fail and the surviving neighbor fibers have to share a larger fraction of that transferred from the failed fiber. The extreme case is that of local load-sharing model, where load of the failed spring or fiber is shared (usually equally) by the surviving nearest neighbor fibers.


Disasters

Failures caused by brittle fracture have not been limited to any particular category of engineered structure. Though brittle fracture is less common than other types of failure, the impacts to life and property can be more severe. The following notable historic failures were attributed to brittle fracture: *Pressure vessels: Great Molasses Flood in 1919, New Jersey molasses tank failure in 1973 *Bridges: King Street Bridge span collapse in 1962,
Silver Bridge The Silver Bridge was an eyebar-chain suspension bridge built in 1928 and named for the color of its aluminum paint. The bridge carried U.S. Route 35 over the Ohio River, connecting Point Pleasant, West Virginia, and Gallipolis, Ohio. On Dec ...
collapse in 1967, partial failure of th
Hoan Bridge
in 2000 *Ships:
Titanic RMS ''Titanic'' was a British passenger liner, operated by the White Star Line, which sank in the North Atlantic Ocean on 15 April 1912 after striking an iceberg during her maiden voyage from Southampton, England, to New York City, United ...
in 1912,
Liberty ships Liberty ships were a ship class, class of cargo ship built in the United States during World War II under the Emergency Shipbuilding Program. Though British in concept, the design was adopted by the United States for its simple, low-cost constr ...
during World War II,
SS Schenectady The SS ''Schenectady'' was a T2-SE-A1 tanker built during World War II for the United States Maritime Commission. She was the first tanker constructed by the Kaiser Shipbuilding Company shipyard at the Swan Island Shipyard in Portland, Orego ...
in 1943


See also

* Environmental stress cracking * Environmental stress fracture *
Fatigue (material) In materials science, fatigue is the initiation and propagation of cracks in a material due to cyclic loading. Once a fatigue crack has initiated, it grows a small amount with each loading cycle, typically producing striations on some parts of ...
*
Forensic engineering Forensic engineering has been defined as ''"the investigation of failures - ranging from serviceability to catastrophic - which may lead to legal activity, including both civil and criminal".'' It includes the investigation of materials, product ...
*
Forensic materials engineering Forensic materials engineering, a branch of forensic engineering, 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 materi ...
*
Fractography Fractography is the study of the 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 fa ...
*
Fracture (geology) A fracture is any separation in a geologic formation, such as a Joint (geology), joint or a Fault (geology), fault that divides the Rock (geology), rock into two or more pieces. A fracture will sometimes form a deep fissure or crevice in the ro ...
*
Fracture (mineralogy) In the field of mineralogy, fracture is the texture and shape of a rock's surface formed when a mineral is fractured. Minerals often have a highly distinctive fracture, making it a principal feature used in their identification. Fracture diffe ...
*
Gilbert tessellation In applied mathematics, a Gilbert tessellation. or random crack network. is a mathematical model for the formation of mudcracks, needle-like crystals, and similar structures. It is named after Edgar Gilbert, who studied this model in 1967.. In Gi ...
*
Microvoid coalescence Microvoid coalescence (MVC) is a high energy microscopic fracture mechanism observed in the majority of metallic alloys and in some engineering plastics. Fracture process MVC proceeds in three stages: nucleation, growth, and coalescence of m ...
* Notch *
Season cracking Season cracking is a form of stress-corrosion cracking of brass cartridge cases originally reported from British forces in India. During the monsoon season, military activity was temporarily reduced, and ammunition was stored in stables until the ...
*
Stress corrosion cracking Stress corrosion cracking (SCC) is the growth of crack formation in a corrosive environment. It can lead to unexpected and sudden failure of normally ductile metal alloys subjected to a tensile stress, especially at elevated temperature. SCC ...


Notes


References


Further reading

* Dieter, G. E. (1988) ''Mechanical Metallurgy'' * A. Garcimartin, A. 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.'' * 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
Fracture and Reconstruction of a Clay Bowl
{{Authority control Materials science Building defects Elasticity (physics) Plasticity (physics) Solid mechanics Fracture mechanics Mechanics Glass physics