Definition of Young's Modulus
For solids that obey Hooke's Law:
Young's Modulus (E) is the ratio of tensile stress (s) to tensile strain (e) in a specimen subject to uniaxial tension.
This definition then begs for definitions of the terms within it.
For a force tending to elongate a specimen, the tensile stress is the ratio of the *force* (F) applied in a particular direction in the specimen to the cross-sectional area (A) of the specimen in a plane normal to the direction of the applied force.
(* Strictly speaking, to achieve equilibrium this has to be a pair of equal and opposite forces acting along that direction.)
[If the direction of application of the force is reversed so that the force tends to shorten the sample, the stress is called "compressive".]
If an increment in the tensile stress applied to a specimen of length (l) produces an increment in length (dl) parallel to the direction of application of the stress, the increment in tensile strain (de) is given by
and the "true" or "logarithmic" tensile strain (e) is given by
For small strains it is often sufficient to approximate the true strain by the "nominal" or "engineering" strain (e)
Uniaxial tension means that the only externally applied forces acting on the specimen are a pair of equal and opposite forces acting along a line.
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