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Christensen Failure Criterion
The Christensen failure criterion is a material failure theory for isotropic materials that attempts to span the range from ductile to brittle materials. It has a two-property form calibrated by the uniaxial tensile and compressive strengths T \left (\sigma_T\right ) and C \left (\sigma_C\right ). The theory was developed by Stanford professor Richard. M. Christensen and first published in 1997. Description The Christensen failure criterion is composed of two separate subcriteria representing competitive failure mechanisms. when expressed in principal stress components, it is given by : ;Polynomial invariants failure criterion For 0\le\frac\le1 ;Coordinated Fracture Criterion For 0\le \frac\le \frac The geometric form of () is that of a paraboloid in principal stress space. The fracture criterion () (applicable only over the partial range 0 ≤ T/C ≤ 1/2 ) cuts slices off the paraboloid, leaving three flattened elliptical surfaces on it. The fracture cut ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Material Failure Theory
Material failure theory is an interdisciplinary field of materials science and solid mechanics which attempts to predict the conditions under which solid materials fail under the action of external loads. The failure of a material is usually classified into brittle failure (fracture) or ductile failure ( yield). Depending on the conditions (such as temperature, state of stress, loading rate) most materials can fail in a brittle or ductile manner or both. However, for most practical situations, a material may be classified as either brittle or ductile. In mathematical terms, failure theory is expressed in the form of various failure criteria which are valid for specific materials. Failure criteria are functions in stress or strain space which separate "failed" states from "unfailed" states. A precise physical definition of a "failed" state is not easily quantified and several working definitions are in use in the engineering community. Quite often, phenomenological failu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Von Mises Yield Criterion
The maximum distortion criterion (also von Mises yield criterion) states that yielding of a ductile material begins when the second invariant of deviatoric stress J_2 reaches a critical value. It is a part of plasticity theory that mostly applies to ductile materials, such as some metals. Prior to yield, material response can be assumed to be of a nonlinear elastic, viscoelastic, or linear elastic behavior. In materials science and engineering von Mises yield criterion is also formulated in terms of the von Mises stress or equivalent tensile stress, \sigma_\text. This is a scalar value of stress that can be computed from the Cauchy stress tensor. In this case, a material is said to start yielding when the von Mises stress reaches a value known as yield strength, \sigma_\text. The von Mises stress is used to predict yielding of materials under complex loading from the results of uniaxial tensile tests. The von Mises stress satisfies the property where two stress states with equa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Plasticity (physics)
In physics and materials science, plasticity, also known as plastic deformation, is the ability of a solid material to undergo permanent Deformation (engineering), deformation, a non-reversible change 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 material itself. In engineering, the transition from Elasticity (physics), elastic behavior to plastic behavior is known as Yield (engineering), yielding. Plastic deformation is observed in most materials, particularly metals, soils, Rock (geology), rocks, concrete, and foams. However, the physical mechanisms that cause plastic deformation can vary widely. At a crystalline scale, plasticity in metals is usually a consequence of dislocations. Such defects are relatively rare in most crystalline materials, but are numerous in some and part of their crystal structure; in such cases, plastic crystallinity can res ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mechanical Failure
Structural integrity and failure is an aspect of engineering that deals with the ability of a structure to support a designed structural load (weight, force, etc.) without breaking and includes the study of past structural failures in order to prevent failures in future designs. Structural integrity is the ability of an item—either a structural component or a structure consisting of many components—to hold together under a load, including its own weight, without breaking or deforming excessively. It assures that the construction will perform its designed function during reasonable use, for as long as its intended life span. Items are constructed with structural integrity to prevent catastrophic failure, which can result in injuries, severe damage, death, and/or monetary losses. ''Structural failure'' refers to the loss of structural integrity, or the loss of load-carrying capacity in either a structural component or the structure itself. Structural failure is initiated whe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mohr–Coulomb Theory
Mohr–Coulomb theory is a mathematical model (see yield surface) describing the response of brittle materials such as concrete, or rubble piles, to shear stress as well as normal stress. Most of the classical engineering materials follow this rule in at least a portion of their shear failure envelope. Generally the theory applies to materials for which the compressive strength far exceeds the tensile strength. In geotechnical engineering it is used to define shear strength of soils and rocks at different effective stresses. In structural engineering it is used to determine failure load as well as the angle of fracture of a displacement fracture in concrete and similar materials. Coulomb's friction hypothesis is used to determine the combination of shear and normal stress that will cause a fracture of the material. Mohr's circle is used to determine which principal stresses will produce this combination of shear and normal stress, and the angle of the plane in which this ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Strength Of Materials
The field of strength of materials, also called mechanics of materials, typically refers to various methods of calculating the stresses and strains in structural members, such as beams, columns, and shafts. The methods employed to predict the response of a structure under loading and its susceptibility to various failure modes takes into account the properties of the materials such as its yield strength, ultimate strength, Young's modulus, and Poisson's ratio. In addition, the mechanical element's macroscopic properties (geometric properties) such as its length, width, thickness, boundary constraints and abrupt changes in geometry such as holes are considered. The theory began with the consideration of the behavior of one and two dimensional members of structures, whose states of stress can be approximated as two dimensional, and was then generalized to three dimensions to develop a more complete theory of the elastic and plastic behavior of materials. An important founding pion ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Composite Material
A composite material (also called a composition material or shortened to composite, which is the common name) is a material which is produced from two or more constituent materials. These constituent materials have notably dissimilar chemical or physical properties and are merged to create a material with properties unlike the individual elements. Within the finished structure, the individual elements remain separate and distinct, distinguishing composites from mixtures and solid solutions. Typical engineered composite materials include: *Reinforced concrete and masonry *Composite wood such as plywood *Reinforced plastics, such as fibre-reinforced polymer or fiberglass *Ceramic matrix composites ( composite ceramic and metal matrices) *Metal matrix composites *and other advanced composite materials There are various reasons where new material can be favoured. Typical examples include materials which are less expensive, lighter, stronger or more durable when compared with commo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ductility
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 stress before failure. Ductility is an important consideration in engineering and manufacturing. It defines a material's suitability for certain manufacturing operations (such as cold working) and its capacity to absorb mechanical overload.. Some metals that are generally described as ductile include gold and copper. However, not all metals experience ductile failure as some can be characterized with brittle failure like cast iron. Polymers generally can be viewed as ductile materials as they typically allow for plastic deformation. Malleability, a similar mechanical property, is characterized by a material's ability to deform plastically without failure under compressive stress. Historically, materials were considered malleable if they were am ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fracture
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. 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, which charts the stress–strain cu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ductility
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 stress before failure. Ductility is an important consideration in engineering and manufacturing. It defines a material's suitability for certain manufacturing operations (such as cold working) and its capacity to absorb mechanical overload.. Some metals that are generally described as ductile include gold and copper. However, not all metals experience ductile failure as some can be characterized with brittle failure like cast iron. Polymers generally can be viewed as ductile materials as they typically allow for plastic deformation. Malleability, a similar mechanical property, is characterized by a material's ability to deform plastically without failure under compressive stress. Historically, materials were considered malleable if they were am ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Christensen Fig 1
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Christensen may refer to: * Christensen (surname) * Christensen (constructor), a former racing car constructor * 164P/Christensen, a periodic comet * 170P/Christensen, a periodic comet See also *Christiansen *Christianson *Kristiansen Kristiansen () is a Danish and Norwegian patronymic surname that may refer to the following notable people: *Celine Lundbye Kristiansen, Danish handball player * Egil Kristiansen, Norwegian cross country skier * Einar Kristiansen, Norwegian Nordic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stress (mechanics)
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 elongation which is also known as deformation, like the stretching of an elastic band, it is called tensile stress. But, when the forces result in the compression of an object, it is called compressive stress. It results when forces like tension or compression act on a body. The greater this force and the smaller the cross-sectional area of the body on which it acts, the greater the stress. Therefore, stress is measured in newton per square meter (N/m2) or pascal (Pa). Stress expresses the internal forces that neighbouring particles of a continuous material exert on each other, while strain is the measure of the deformation of the material. For example, when a solid vertical bar is supporting an overhead weight, each particle in the bar pushe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
