thumb|Ductile failure of a metallic specimen strained axially
Fracture is the cracking or breaking into pieces of an object or material under the action of stress. The science of fracture is a field of study in physics and engineering.
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.
Brittle fractures occur without any 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
thumb|Stress vs. strain curve typical of aluminum
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 (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. Similar observations were made by Galileo Galilei 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).
Types
There are two types of fractures: brittle and ductile fractures respectively without or with plastic deformation prior to failure.
===Brittle===<!-- This section is linked from Ceramic -->
thumb|right|Brittle fracture in glass
thumb|right|alt=A roughly ovoid metal cylinder, viewed end-on. The bottom-right portion of the metal's end surface is dark and slightly disfigured, whereas the rest is a much lighter colour and not disfigured.|Fracture of an aluminum [[crank arm of a bicycle, where the bright areas display a brittle fracture, and the dark areas show fatigue fracture]]
In brittle fracture, no apparent plastic deformation takes place before fracture. Brittle fracture typically involves little energy absorption and occurs at high speeds—up to in steel.
:<math>\sigma_\mathrm{elliptical\ crack} = \sigma_\mathrm{applied}\left(1 + 2 \sqrt{ \frac{a}{\rho\right)= 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 gets
:<math>\sigma_\mathrm{fracture} = \sqrt{ \frac{E \gamma \rho}{4 a r_o.</math>
Sharp cracks (small <math>\rho</math>) and large defects (large <math>a</math>) both lower the fracture strength of the material.
As of 2010 scientists discovered supersonic fracture, the phenomenon of crack propagation faster than the speed of sound in a material. This phenomenon has also been verified by experiment with 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.
left|thumb|Ductile fracture surface of 6061-T6 aluminum
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 microvoid formation, microvoid coalescence (also known as crack formation), crack propagation, and failure, often resulting in a cup-and-cone shaped failure surface. The microvoids nucleate at various internal discontinuities, such as precipitates, secondary phases, inclusions, and grain boundaries in the material.
The microvoid coalescence results in a dimpled appearance on the fracture surface. The dimple shape is heavily influenced by the type of loading. Fracture under local uniaxial tensile loading usually results in formation of equiaxed dimples. Failures caused by shear will produce elongated or parabolic shaped dimples that point in opposite directions on the matching fracture surfaces. Finally, tensile tearing produces elongated dimples that point in the same direction on matching fracture surfaces. Cyclical prestressing the sample can then induce a fatigue crack which extends the crack from the fabricated notch length of <math display="inline">\mathrm{c\prime}</math> to <math display="inline">\mathrm{c}</math>. This value <math display="inline">\mathrm{c}</math> is used in the above equations for determining <math display="inline">\mathrm{K}_\mathrm{c}</math>.
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, <math display="inline">\mathrm{K}_\mathrm{c}</math> 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 <math display="inline">\mathrm{K}_\mathrm{c}</math> values that are ~5% of that found in metals. 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. 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.
Most used computational numerical methods are finite element and boundary integral equation methods. Other methods include stress and displacement matching, element crack advance in which latter two come under Traditional Methods in Computational Fracture Mechanics.
thumb|Fine Mesh done in Rectangular area in Ansys software (Finite Element Method)
The finite element method
The structures are divided into discrete elements of 1-D beam, 2-D plane stress or plane strain, 3-D bricks or tetrahedron types. The continuity of the elements are enforced using the nodes.