Elastic Moduli - Young’s Modulus

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Notes

Elastic Modulus

Elastic modulus is the ratio of stress and strain.
Elastic modulus is a characteristic value of each material. This means gold will have a specific value of elastic modulus and rubber will have a specific value of elastic modulus etc.
`"k"="Stress"/"Strain"` Where k= Elastic modulus.

Types of elastic modulus:

1. Young’s Modulus:

Young’s modulus is derived from the name of the scientist who defined it.

It is the ratio of longitudinal stress to longitudinal strain.
It is denoted by Y.
Mathematically:
`"Y"= "longitudinal stress"/ "longitudinal strain" = σ/ ε`
`= ("F"/"A")/((Δ"L")/"L")`
`"Y"="FL"/(Δ"L")`
If Young’s modulus is more, to produce a small change in length more force required.
S.I. unit is `"Nm"^(–2)` or Pascal (Pa).
Metals have comparatively greater Young’s Modulus. To change the length of metals, greater force is required.

Young’s Modulus: Application

In industrial construction, steel is preferred over copper. The reason behind this is steel is more elastic than copper.
If there is slight deformation in steel due to contraction and expansion it will come back to its original position.
Steel is preferred over copper to construct bridges.

Substance	Density rho `("kgm"^-3)`	Youngs modulus Y `(10^9"Nm"^-2)`	Ultimate strength, `sigma_u(10^6"Nm"^-2)`	Yield strength `sigma_y(10^6"Nm"^-2)`
Aluminum	2710	70	110	95
Copper	8890	110	400	200
Iron (wrought)	7800-7900	190	330	170
Steel	7860	200	400	250
Glass	2190	65	50	-
Concrete	2320	30	40	-
Wood	525	13	50	-
Bone	1900	9.4	170	-
Polystyrene	1050	3	48	-