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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, 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 s ...
. 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 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 ...
.

# 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 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 ...
(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 ...
(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, 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

# 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. Strai ...
prior to failure.

## Brittle

In brittle 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. Strai ...
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 solids, 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 in 1921: :$\sigma_\mathrm= \sqrt$ where: – :$E$ is the Young's modulus of the material, :$\gamma$ is the
surface energy In surface science, surface free energy (also interfacial free energy or surface energy) quantifies the disruption of intermolecular bonds that occurs when a surface is created. In solid-state physics, surfaces must be intrinsically less ener ...
, 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 :$\sigma_\mathrm= \sigma_\mathrm\left\left(1 + 2 \sqrt\right\right)= 2 \sigma_\mathrm \sqrt$ (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 Supersonic fractures are fractures where the fracture propagation velocity is higher 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 ( Markus ...
, 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 (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 fracture, extensive plastic deformation ( necking) takes place before fracture. The terms "rupture" and "ductile rupture" describe the ultimate failure 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 s ...
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 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 o ...
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 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, Unite ...
in 1912, Liberty ships during World War II, SS Schenectady in 1943

*
Environmental stress cracking Environmental Stress Cracking (ESC) is one of the most common causes of unexpected brittle failure of thermoplastic (especially amorphous) polymers known at present. According to ASTM D883, stress cracking is defined as "an external or inter ...
* Environmental stress fracture * Fatigue (material) *
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, produ ...
* Forensic materials engineering * Fractography * Fracture (geology) *
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 differ ...
* Gilbert tessellation *
Microvoid coalescence Microvoid coalescence (MVC) is a high energy microscopic fracture mechanism observed in the majority of alloy, metallic alloys and in some engineering plastics. Fracture process MVC proceeds in three stages: nucleation, growth, and coalescence ...
* 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 th ...
*
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 ...