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Strength of materials is Materials Science applied to the study of engineering materials and their mechanical behavior in general (such as Stress , Deformation , Strain and stress-strain relations). Strength is considered in terms of Compressive Strength , Tensile Strength , and Shear Strength , namely the limit states of Compressive Stress , Tensile Stress and Shear Stress respectively. Strength can be simply defined as the ability of a material to resist the application of force. The effects of dynamic loading is probably the most important practical part of the strength of materials, especially the problem of Fatigue . Repeated loading often initiates brittle cracks, which grow slowly until failure occurs. DEFINITIONS Stress terms Uniaxial stress is expressed by : where F is the force (N) acting on an area A (m^2). The area can be the undeformed area or the deformed area, depending on whether Engineering Stress or true stress is used.
Strength terms '' Yield Strength '' is the lowest stress that gives permanent deformation in a material. In some materials, like Aluminium Alloy s, the point of yielding is hard to define, thus it is usually given as the stress required to cause 0.2% plastic strain. '' Compressive Strength '' is a limit state of Compressive Stress that leads to compressive failure in the manner of ductile failure (infinite theoretical yield) or in the manner of brittle failure (rupture as the result of crack propagation, or sliding along a weak plane - see Shear Strength ). '' Tensile Strength '' or ''ultimate tensile strength'' is a limit state of Tensile Stress that leads to tensile failure in the manner of ductile failure (yield as the first stage of failure, some hardening in the second stage and break after a possible "neck" formation) or in the manner of brittle failure (sudden breaking in two or more pieces with a low stress state). Tensile strength can be given as either true stress or engineering stress. '' Fatigue Strength '' is a measure of the strength of a material or a component under cyclic loading, and is usually more difficult to assess than the static strength measures. Fatigue strength is given as stress amplitude or stress range (), usually at zero mean stress, along with the number of cycles to failure. '' Impact Strength '', often measured with the Izod Impact Strength Test or Charpy Impact Test , both of which measure the impact energy required to fracture a sample. Strain - deformation terms '' Deformation '' of the material is the change in geometry when stress is applied (in the form of force loading, gravitational field, acceleration, thermal expansion, etc.). Deformation is expressed by the displacement field of the material. '' Strain '' or ''reduced deformation'' is a mathematical term to express the trend of the deformation change among the material field. For uniaxial loading - displacements of a specimen (for example a bar element) it is expressed as the quotient of the displacement and the length of the specimen. For 3D displacement fields it is expressed as derivatives of displacement functions in terms of a second order Tensor (with 6 independent elements). '' Deflection '' is a term to describe the magnitude to which a structural element bends under a load. STRESS-STRAIN RELATIONS '' Elasticity '' is the ability of a material to return to its previous shape after stress is released. In many materials, the relation between applied stress and the resulting strain is directly proportional (up to a certain limit), and a graph representing those two quantities is a straight line. The slope of this line is known as Young's Modulus , or the "Modulus of Elasticity." The Modulus of Elasticity can be used to determine stress-strain relationships in the linear-elastic portion of the stress-strain curve. The linear-elastic region is taken to be between 0 and 0.2% strain, and is defined as the region of strain in which no yielding (permanent deformation) occurs. '' Plasticity '' or plastic deformation is the opposite of elastic deformation and is accepted as unrecoverable strain. Plastic deformation is retained even after the relaxation of the applied stress. Most materials in the linear-elastic category are usually capable of plastic deformation. Brittle materials, like ceramics, do not experience any plastic deformation and will fracture under relatively low stress. Materials such as metals usually experience a small amount of plastic deformation before failure while soft or ductile polymers will plasticly deform much more. Consider the difference between a fresh carrot and chewed bubble gum. The carrot will stretch very little before breaking, but nevertheless will still stretch. The chewed bubble gum, on the other hand, will plasticly deform enormously before finally breaking. DESIGN TERMS Ultimate strength is an attribute directly related to a material, rather than just specific specimen of the material, and as such is quoted force per unit of cross section area (N/m&2). For example, the ultimate tensile strength (UTS) of AISI 1018 Steel is 440 MN /m&2. In general, the SI unit of stress is the Pascal , where 1 Pa = 1 N/m&2. In English units, the unit of stress is given as lbf/in&2 or Pounds-force Per Square Inch . This unit is often abbreviated as psi. One thousand psi is abbreviated '''ksi'''. Factor Of Safety is a design constraint that an engineered component or structure must achieve. , where FS: the Factor of Safety, R: The applied stress, and UTS: the Ultimate force (or stress). Margin of Safety is also sometimes used to as design constraint. It is defined MS=Factor of safety - 1 For example to achieve a factor of safety of 4, the allowable stress in an AISI 1018 steel component can be worked out as = 440/4 = 110 MPa, or = 110×106 N/m&2. SUGGESTED READING
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