Modulus of Elasticity-Young's Modulus, Modulus of Elasticity, E

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Definition of Modulus of Elasticity (Young's Modulus) #

The modulus of elasticity is the constant of the deformation produced by a given stress acting on a material. According to Hooke's law, for the elastic deformation phase of a material, the stress is directly proportional to the strain.

Hooke's law is expressed as:

σ = Eε

In the above equation, "E" is referred to as the modulus of elasticity, σ denotes stress and ε denotes strain.

We can write an expression for the modulus of elasticity using the equation above:

E = (F*L)/(A*δL)

Therefore, we can define the modulus of elasticity as the ratio of normal stress to longitudinal strain.

Modulus of elasticity unit #

Normal stresses have units of Pascal Pa and longitudinal strains have no units. This is because the longitudinal strain is the ratio of the change in length to the original length. So the unit of modulus of elasticity is the same as the unit of stress, which is Pascal (Pa). We usually use megapascals (MPa) and gigapascals (GPa) to measure the modulus of elasticity.

How to measure Young's modulus or modulus of elasticity? #

Let us take an example of a rod of ductile material made of mild steel. Now perform a tensile test on a universal testing machine. After the tensile test, the stress-strain diagram is plotted and the following curve is obtained.

From the curve, from point O to point B, the region is an elastic region. Then, plastic deformation begins. The point A in the curve represents the proportional limit. For this curve, we can write the value of the modulus of elasticity (E) equal to the slope of the stress-strain curve up to A.

If the value of E increases, the longitudinal strain decreases, which means that the length change decreases.

Some common sense laws of modulus of elasticity #

The lower the modulus of elasticity, the greater the relative amount of deformation, the smaller the stiffness, the material is easy to deform the better the flexibility; the higher the modulus of elasticity, the material deformation of the modulus of elasticity is relatively small, the stiffness is large, the material is not easy to deform, the more brittle. Modulus of elasticity can be regarded as a measure of the material to produce elastic deformation of the degree of difficulty of the index, the larger the value, so that the material to produce a certain elastic deformation of the stress is also the greater, that is, the greater the material stiffness, that is, in a certain amount of stress, the occurrence of elastic deformation of the smaller. Apply an external force to the elastomer, the elastomer will undergo a change in shape, called "strain".

Relationship between modulus of elasticity and brittleness #

Brittle materials are those with elongation less than 3%. And the elastic material refers to the plastic deformation under a certain external force. Brittle materials can be low modulus of elasticity, such as glass, but high modulus of elasticity is not necessarily a brittle material, such as mild steel, alloy steel and so on.

Other information about modulus of elasticity #

• Both the modulus of elasticity and Young's modulus are the same. The modulus of elasticity is a constant; it depends on temperature and pressure.
• The values of the modulus of elasticity and E depend only on the material and not on its geometry (the modulus of elasticity changes when a wire is bent into a spring).
• The modulus of elasticity can be used to calculate how much a material will stretch and how much potential energy it will store

Modulus of elasticity of common metals and non-metals #

Material name Modulus of elasticity E (Gpa)
Diamond 1100
Gray cast iron 118-126
White cast iron 113-157
Ductile iron 173
Ductile iron 120
Magnesium 45
Magnesium alloy 1.74
Titanium (Ti) 105-120
Carbon steel 206
Cast steel 202
Nickel-chromium steel 206
Alloy steel 206
High speed steel (including WW9%) 8.3
High speed steel (including WW18%) 8.7
Rolled pure copper (purple copper) 108
Cold-drawn pure copper (purple copper) 127
Rolled Phosphor Tin Bronze 113
Cold-drawn brass 89-97
Cast brass 8.62
Rolled manganese bronze 108
Cast tin bronze 103
Cast Aluminum Bronze 103
Aluminum, aluminum-nickel alloys for industrial use 2.7
Castable aluminum alloy 2.7
Rolled aluminum 68
Drawn aluminum wire 69
Hard Aluminum Alloy 70
Rolled zinc 82
Lead 16
Tungsten (W) 400-410
Tungsten carbide (WC) 450-650
Nickel 8.9
Gold 19.32
Silver 10.5
Tin 7.29
Mercury 13.55
Silicon Carbide (SiC) 450
Silicon copper sheet 7.55-7.8
Tin-based bearing alloys 7.34-7.75
Lead-based bearing alloys 9.33-10.67
Cemented carbide (tungsten-cobalt) 14.4-14.9
Tungsten-cobalt-titanium carbide 9.5-12.4
Diamond 1,050-1,200
Glass 55
Plexiglass (PMMA) 2.35-29.42
Rubber 0.0078
Glueboard, fiberboard 1.3-1.4
Bakelite 1.96-2.94
Phenolic Plastic with Cloth 3.92-8.83
Celluloid 1.71-1.89
ABS 0.2
ABS, PC 2.41
Polypropylene PP 1.5-2
PP copolymer 0.896
Nylon 1010 1.07
Nylon 66 8.3
PA6 2.32
PE high density 1.07
PE low/medium density 0.172
Low pressure polyethylene PE 0.54-0.75
High pressure polyethylene PE 0.147-0.245
Rigid polyvinyl chloride (PVC) 3.14-3.92
Polystyrene 0.91
Polytetrachloroethylene 1.14-1.42
Acrylic (medium impact resistance) 2.4
PBT 1.93
POM acetalized copolymer 2.6
P/S medium-high flow 2.28 0.8173 0.387
PVC0.007 Plasticized 0.006
PVC rigidity 2.41
Polyethylene terephthalate PET 2-2.5
Polystyrene PS 3-3.5
Carbon fiber reinforced plastic (unidirectional granular surface) 150
Concrete 13.73-39.2