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Tsai–Wu Failure Criterion
The Tsai–Wu failure criterion is a phenomenological material failure theory which is widely used for anisotropic composite materials which have different strengths in tension and compression. The Tsai-Wu criterion predicts failure when the failure index in a laminate reaches 1. This failure criterion is a specialization of the general quadratic failure criterion proposed by Gol'denblat and Kopnov and can be expressed in the form : F_i~\sigma_i + F_~\sigma_i~\sigma_j \le 1 where ij=1\dots 6 and repeated indices indicate summation, and F_i, F_ are experimentally determined material strength parameters. The stresses \sigma_i are expressed in Voigt notation. If the failure surface is to be closed and convex, the interaction terms F_ must satisfy : F_F_ - F_^2 \ge 0 which implies that all the F_ terms must be positive. Tsai–Wu failure criterion for orthotropic materials For orthotropic materials with three planes of symmetry oriented with the coordinate directions, if w ... [...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 failure ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Composite Material
A composite or composite material (also composition material) 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. Composite materials with more than one distinct layer are called ''composite laminates''. Typical engineered composite materials are made up of a binding agent forming the ''matrix'' and a Filler (materials), filler material (particulates or fibres) giving ''substance'', e.g.: * Concrete, reinforced concrete and masonry with cement, lime or Mortar (masonry), mortar (which is itself a composite material) as a binder * Composite wood such as glulam and plywood with wood glue as a binder * Reinforced plastics, such as fiberglass and fibre-rein ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Voigt Notation
In mathematics, Voigt notation or Voigt form in multilinear algebra is a way to represent a symmetric tensor by reducing its order. There are a few variants and associated names for this idea: Mandel notation, Mandel–Voigt notation and Nye notation are others found. Kelvin notation is a revival by Helbig of old ideas of Lord Kelvin. The differences here lie in certain weights attached to the selected entries of the tensor. Nomenclature may vary according to what is traditional in the field of application. The notation is named after physicists Woldemar Voigt & John Nye (scientist). For example, a 2×2 symmetric tensor ''X'' has only three distinct elements, the two on the diagonal and the other being off-diagonal. Thus its rank can be reduced by expressressing it as a vector without loss of information: X = \begin x_ & x_ \\ x_ & x_ \end = \begin x_ \\ x_ \\ x_ \end. Voigt notation is used in materials science to simplify the representation of the rank-2 stress and strai ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Orthotropic Material
In material science and solid mechanics, orthotropic materials have material properties at a particular point which differ along three orthogonal axes, where each axis has twofold rotational symmetry. These directional differences in strength can be quantified with Hankinson's equation. They are a subset of anisotropic materials, because their properties change when measured from different directions. A familiar example of an orthotropic material is wood. In wood, one can define three mutually perpendicular directions at each point in which the properties are different. It is most stiff (and strong) along the grain (axial direction), because most cellulose fibrils are aligned that way. It is usually least stiff in the radial direction (between the growth rings), and is intermediate in the circumferential direction. This anisotropy was provided by evolution, as it best enables the tree to remain upright. Because the preferred coordinate system is cylindrical-polar, this type of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hill Yield Criteria
The Hill yield criterion developed by Rodney Hill, is one of several yield criteria for describing anisotropic plastic deformations. The earliest version was a straightforward extension of the von Mises yield criterion and had a quadratic form. This model was later generalized by allowing for an exponent ''m''. Variations of these criteria are in wide use for metals, polymers, and certain composites. Quadratic Hill yield criterion The quadratic Hill yield criterion has the form : F(\sigma_-\sigma_)^2 + G(\sigma_-\sigma_)^2 + H(\sigma_-\sigma_)^2 + 2L\sigma_^2 + 2M\sigma_^2 + 2N\sigma_^2 = 1 ~. Here ''F, G, H, L, M, N'' are constants that have to be determined experimentally and \sigma_ are the stresses. The quadratic Hill yield criterion depends only on the deviatoric stresses and is pressure independent. It predicts the same yield stress in tension and in compression. Expressions for ''F'', ''G'', ''H'', ''L'', ''M'', ''N'' If the axes of material anisotropy are assu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polyvinylchloride
Polyvinyl chloride (alternatively: poly(vinyl chloride), colloquial: vinyl or polyvinyl; abbreviated: PVC) is the world's third-most widely produced synthetic polymer of plastic (after polyethylene and polypropylene). About 40 million tons of PVC are produced each year. PVC comes in rigid (sometimes abbreviated as RPVC) and flexible forms. Rigid PVC is used in construction for pipes, doors and windows. It is also used in making plastic bottles, packaging, and bank or membership cards. Adding plasticizers makes PVC softer and more flexible. It is used in plumbing, electrical cable insulation, flooring, signage, phonograph records, inflatable products, and in rubber substitutes. With cotton or linen, it is used in the production of canvas. Polyvinyl chloride is a white, brittle solid. It is soluble in ketones, chlorinated solvents, dimethylformamide, THF and DMAc. Discovery PVC was synthesized in 1872 by German chemist Eugen Baumann after extended investigation and experime ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Trabecular Bone
A trabecula (: trabeculae, from Latin for 'small beam') is a small, often microscopic, tissue element in the form of a small beam, strut or rod that supports or anchors a framework of parts within a body or organ. A trabecula generally has a mechanical function, and is usually composed of dense collagenous tissue (such as the trabecula of the spleen). It can be composed of other material such as muscle and bone. In the heart, muscles form trabeculae carneae and septomarginal trabeculae, and the left atrial appendage has a tubular trabeculated structure. Cancellous bone is formed from groupings of trabeculated bone tissue. In cross section, trabeculae of a cancellous bone can look like septa, but in three dimensions they are topologically distinct, with trabeculae being roughly rod or pillar-shaped and septa being sheet-like. When crossing fluid-filled spaces, trabeculae may offer the function of resisting tension (as in the penis, see for example trabeculae of corpora c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cancellous Bone
A bone is a rigid organ that constitutes part of the skeleton in most vertebrate animals. Bones protect the various other organs of the body, produce red and white blood cells, store minerals, provide structure and support for the body, and enable mobility. Bones come in a variety of shapes and sizes and have complex internal and external structures. They are lightweight yet strong and hard and serve multiple functions. Bone tissue (osseous tissue), which is also called bone in the uncountable sense of that word, is hard tissue, a type of specialised connective tissue. It has a honeycomb-like matrix internally, which helps to give the bone rigidity. Bone tissue is made up of different types of bone cells. Osteoblasts and osteocytes are involved in the formation and mineralisation of bone; osteoclasts are involved in the resorption of bone tissue. Modified (flattened) osteoblasts become the lining cells that form a protective layer on the bone surface. The mineralised ... [...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 failure ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Yield (engineering)
In materials science and engineering, the yield point is the point on a stress–strain curve that indicates the limit of elastic behavior and the beginning of plastic behavior. Below the yield point, a material will deform elastically and will return to its original shape when the applied stress is removed. Once the yield point is passed, some fraction of the deformation will be permanent and non-reversible and is known as plastic deformation. The yield strength or yield stress is a material property and is the stress corresponding to the yield point at which the material begins to deform plastically. The yield strength is often used to determine the maximum allowable load in a mechanical component, since it represents the upper limit to forces that can be applied without producing permanent deformation. For most metals, such as aluminium and cold-worked steel, there is a gradual onset of non-linear behavior, and no precise yield point. In such a case, the offset yield p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Engineering Failures
Engineering is the practice of using natural science, mathematics, and the engineering design process to Problem solving#Engineering, solve problems within technology, increase efficiency and productivity, and improve Systems engineering, systems. Modern engineering comprises many subfields which include designing and improving infrastructure, machinery, vehicles, electronics, Materials engineering, materials, and energy systems. The Academic discipline, discipline of engineering encompasses a broad range of more Academic specialization, specialized fields of engineering, each with a more specific emphasis for applications of applied mathematics, mathematics and applied science, science. See glossary of engineering. The word '':wikt:engineering, engineering'' is derived from the Latin . Definition The American Engineers' Council for Professional Development (the predecessor of the Accreditation Board for Engineering and Technology aka ABET) has defined "engineering" as: ... [...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 resul ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
