Stress (physics)

In physics, stress is the internal distribution of forces within a body that balance and react to the loads applied to it. Stress is a tensor quantity with nine terms, but can be described fully by six terms due to symmetry. Simplifying assumptions are often used to represent stress as a vector for engineering calculations.

Stress in one-dimensional bodies

The idea of stress originates in two simple, but important, observations of the loading (in tension) of a one-dimensional body, for example, a steel wire.

Related Topics:
Steel - Wire

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

• When a wire is pulled tight, it stretches (undergoes strain). The amount it stretches is proportional to the load divided by the cross-sectional area of the wire, σ = F/A.
• Failure occurs when the load exceeds a critical value for the material, the tensile strength multiplied by the cross-sectional area of the wire, F_c = σ_t A.

These observations suggest that the fundamental characteristic that affects the deformation and failure of materials is stress, force divided by the area over which it is applied.

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

This definition of stress, σ = F/A, is sometimes called engineering stress and is used for rating the strength of materials loaded in one dimension. The cross-sectional area is measured prior to applying strain for testing. Poisson's ratio, however, reveals that any applied strain will produce a change in the area, A. Engineering stress neglects this change in area. Stress-strain diagrams are usually presented as engineering stress, even though the sample may undergo a substantial change in cross-sectional area during testing.

Related Topics:
Strain - Poisson's ratio - Stress-strain diagrams

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

True stress is a simplified definition of stress that includes the change in cross-sectional area. Both engineering stress and true stress should be evaluated as tensors for three-dimensional cases.

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

The distinction between engineering and true stresses is especially important for rubber-like substances and for plasticity, since in these cases the changes in cross-sectional areas can be significant.

Related Topics:
Rubber - Plasticity

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

An example; a steel bolt of diameter 5 mm, has a cross-sectional area of 19.6 mm2. A load of 50 N induces a stress (force distributed over the cross section) of σ = 50/19.6 = 2.55 MPa (N/mm2). This can be thought of as each square millimeter of the bolt supporting 2.55 N of the total load. In another bolt with half the diameter, and hence a quarter the cross-sectional area, carrying the same 50 N load, the stress will be quadrupled (10.2 MPa).

Related Topics:
Steel - Bolt - Diameter - Mm - Area - N - MPa

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

The ultimate tensile strength is a property of a material loaded in one dimension. It allows the calculation of the load that would cause fracture. The compressive strength is a similar property for compressive loads. The yield tensile strength is the value of stress causing plastic deformation. These values are determined experimentally using the measurement procedure known as the tensile test.

Related Topics:
Tensile strength - Fracture - Compressive strength - Yield - Plastic deformation - Measurement - Tensile test

~ ~ ~ ~ ~ ~ ~ ~ ~ ~