Strength of materials

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

Definitions

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 complex 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. A simple case of compression is the uniaxial compression induced by the action of opposite, pushing forces. Compressive strength for materials is generally higher than that of the tensile stress, but geometry is very important in the analysis of compressive stresses.

Tensile stress is a loading that tends to produce stretching of a material by the application of axially directed pulling forces. Any material which falls into the "elastic" category can generally tolerate mild tensile stresses while materials such as ceramics and brittle alloys are very succeptable to failure these same conditions. If a material is stressed beyond its limits, it will fail. The failure mode, either ductile or brittle, is based mostly on the microstructure of the material. Some Steel alloys are examples of materials with high tensile strengh.

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.

Strength terms

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 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).

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.

Stress - strain relations

Elasticity is the ability of a material to return to it 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 more generally the "Modulus of Elasticity" or "Elastic Modulus." This elastic modulus 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 .2% strain, and is defined as the region of strain in which no yielding, or permanent deformation occurs.

Plasticity or plastic deformation is just 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 that reside 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 applied tensile stress. Materials such as metals usually experience a low amount of plastic deformation before failure while soft or ductile polymers will plasticly deform much more.

Consider the difference between a candy bar and chewed bubble gum. A candy bar (not including caramel) 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/m²). For example, the ultimate tensile strength (UTS) of AISI 1018 Steel is 440 MN/m². In general, the SI unit of stress is the pascal, where 1 Pa = 1 N/m². In English units, the unit of stress is given as lbf/in² or pounds-force per square inch. This unit is often abbreviated as "psi" and also "ksi" which represents one-thousand pounds per square inch.

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 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 <math>R = UTS/FS</math> = 440/4 = 110 MPa, or <math>R</math> = 110×10⁶ N/m².

External links

Failure theories

This article is licensed under the GNU Free Documentation License.
It uses material from the Wikipedia article "Strength of materials".