Strength of materials

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Strength of materials is the scientific area of materials science for the study of the strength 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.

1 Definitions
2 Stress - strain relations
3 Design terms
4 Suggested reading
5 External links

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Definitions

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Stress terms

Stress is the internal distribution of forces within a body that balances and reacts to the loads applied to it. It is a complicated tensor quantity that can be broken down into simpler elements for engineering purposes;

Compressive stress (or compression) is the stress state when the material tends to compact (volume decrease). A simple case of compression is the uniaxial compression induced by the action of opposite, pushing forces. Most materials can carry compressive stress, even the granules such as sands.

Tensile stress is a loading that tends to produce stretching on a material by the application of axially directed pulling forces. Materials can withstand some tensile loading, but if enough force is applied, they will eventually break into two parts. Steel is an example of a material with high tensile strength.

Shear stress is caused when a force is applied to produce a sliding failure of a material along a plane that is parallel to the direction of the applied force e.g. when cutting paper with scissors.

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Strength terms

Compressive strength is a limit state of compressive stress that leads to compressive failure in the manner of ductile failure (infinite theoretically yield) or in the manner of brittle failure (rupture as the result of crack propagation, or sliding among a weak plane - see shear strength).

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).

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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 loadings - 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 derivates 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 construction or structural element bends under a load.

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Stress - strain relations

Elasticity is the ability of a material to return to its previous shape after stress is released. In some 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. Hooke's law describes such relationships and is valuable in the study of springs. (see Solid mechanics). In other materials, the relation is not linear. In steel, the most common material for making springs, most of the elastic range is linear, though the relation becomes non-linear at the extreme end, just before the material begins to deform plastically.

Plasticity is the property of materials to deform permanently after force is applied and released. Most solid materials behave elastically when relatively low amounts of force are applied, and plastically under higher amounts of force.

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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 (<math>N/m^2</math>). For example, Ultimate Tensile Strength (UTS) of mild steel is <math>470 MegaN/m^2</math>. It is useful to remember that <math>1 Pa = 1 N/m^2</math>.

Factor of safety is a design constraint that an engineered component or structure must achieve. <math>FS = UTS/R</math>, where FS: the Factor of Safety, R: The acting force (or stress) and UTS: the Ultimate force (or stress).

For example to achieve a factor of safety of 4, the allowable stress in a mild steel component can be worked out as <math>R = UTS/FS = 117.5 MPa</math>.

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