Young's Modulus, Modulus of Elasticity, Shear Modulus, Poisson's Ratio, Density

Metals and Materials Table of Contents

Modulus of Elasticity also know as Young's Modulus is the mathematical description of an object or substance's tendency to be deformed elastically (i.e., non-permanently) when a force is applied to it. The elastic modulus of an object is defined as the slope of its stress-strain curve in the elastic deformation region:

Eq. 1
λ = stress / strain

Where:

λ (lambda) = Elastic Modulus
stress = Restoring force caused due to the deformation divided by the area to which the force is applied
strain = Ratio of the change caused by the stress to the original state of the object

Typical Values Modulus of Elasticity(Young's Modulus)
Material
Modulus of Elasticity, E
(lb/in2 x 106)
Shear Modulus
of Elasticity, G 
(lb/in2 x 106)
Poisson's Ratio
u
Weight Density
(lb/in3)
Aluminum Alloys
10.2
3.9
0.33
0.098
Beryllium Copper
18.0
7.0
0.29
0.30
Carbon Steel
29.0
11.5
0.29
0.28
Cast Iron
14.5
6.0
0.21
0.26
Inconel
31.0
11.5
0.29
0.31
Magnesium
6.5
2.4
0.35
0.07
Molybdenum
48.0
17.1
0.31
0.37
Monel Metal
26.0
9.5
0.32
0.32
Nickel Silver
18.5
7.0
0.32
0.32
Nickel Steel
29.0
11.0
0.29
0.28
Nylon
1.5
0.6
-
0.04
Phosphor Bronze
16.1
6.0
0.35
0.30
Stainless Steel
27.6
10.6
0.31
0.28
Titanium
16.5
6.5
-
0.16

Young’s modulus E for various materials

Figure 1 Young’s modulus E for various materials. (Figure courtesy of Prof. Mike Ashby, Granta Design, Cambridge, U.K.)

Young’s modulus E versus density ρ for various materials. (Figure courtesy of Prof. Mike Ashby, Granta Design, Cambridge, U.K.)
Figure 2 Young’s modulus E versus density ρ for various materials. (Figure courtesy of Prof. Mike Ashby, Granta Design, Cambridge, U.K.)

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