Poisson's Ratio (original) (raw)

When a material is stretched in one direction it tends to get thinner in the other two directions.

When a sample of material is stretched in one direction it tends to get thinner in the lateral direction - and if a sample is compressed in one direction it tends to get thicker in the lateral direction.

Poisson's ratio

Poisson's ratio is

Poisson's Ratio can be expressed as

μ = - εt / εl (1)

where

μ = Poisson's ratio

εt = transverse strain (m/m, ft/ft)

εl = longitudinal or axial strain (m/m, ft/ft)

Strain is defined as "deformation of a solid due to stress".

Longitudinal (or axial) strain can be expressed as

εl = dl / L (2)

where

εl = longitudinal or axial strain (dimensionless - or m/m, ft/ft)

dl = change in length (m, ft)

L = initial length (m, ft)

Contraction (or transverse, lateral or radial) strain can be expressed as

εt = dr / r (3)

where

εt = transverse, lateral or radial strain (dimensionless - or m/m, ft/ft)

dr = change in radius (m, ft)

r = initial radius (m, ft)

Eq. 1, 2 and 3 can be combined to

μ = - ( dr / r ) / ( dl / L ) (4)

Example - Stretching Aluminum

An aluminum bar with length 10 m and radius 100 mm (100 10-3 m) is stretched 5 mm (5 10-3 m) . The radial contraction in lateral direction can be rearranged to

dr = - μ r dl / L (5)

With Poisson's ratio for aluminum 0.334 - the contraction can be calculated as

dr = - 0.334 ( 100 10-3 m ) ( 5 10-3 m) / (10 m)

= 1.7 10 -5 m

= 0.017 mm

Poisson's Ratios for Common Materials

For most common materials the Poisson's ratio is in the range 0 - 0.5 . Typical Poisson's Ratios for some common materials are indicated below.

Poisson's Ratios common Materials

Material Poisson's Ratio - μ -
Upper limit 0.5
Aluminum 0.334
Aluminum, 6061-T6 0.35
Aluminum, 2024-T4 0.32
Beryllium Copper 0.285
Brass, 70-30 0.331
Brass, cast 0.357
Bronze 0.34
Clay 0.41
Concrete 0.1 - 0.2
Copper 0.355
Cork 0
Glass, Soda 0.22
Glass, Float 0.2 - 0.27
Granite 0.2 - 0.3
Ice 0.33
Inconel 0.27 - 0.38
Iron, Cast - gray 0.211
Iron, Cast 0.22 - 0.30
Iron, Ductile 0.26 - 0.31
Iron, Malleable 0.271
Lead 0.431
Limestone 0.2 - 0.3
Magnesium 0.35
Magnesium Alloy 0.281
Marble 0.2 - 0.3
Molybdenum 0.307
Monel metal 0.315
Nickel Silver 0.322
Nickel Steel 0.291
Polystyrene 0.34
Phosphor Bronze 0.359
Rubber 0.48 - ~0.5
Sand 0.29
Sandy loam 0.31
Sandy clay 0.37
Stainless Steel 18-8 0.305
Steel, cast 0.265
Steel, Cold-rolled 0.287
Steel, high carbon 0.295
Steel, mild 0.303
Titanium (99.0 Ti) 0.32
Wrought iron 0.278
Z-nickel 0.36
Zinc 0.331

The relationships between forces, acceleration, displacement, vectors, motion, momentum, energy of objects and more.

Engineering related topics like Beaufort Wind Scale, CE-marking, drawing standards and more.

Plastic deformation properties.

The machinability of some common metals.

The Bulk Modulus - resistance to uniform compression - for some common metals and alloys.

Elastic properties and Young's modulus for metals and alloys like cast iron, carbon steel and more.

Shear Modulus (Modulus of Rigidity) is the elasticity coefficient for shearing or torsion force.

Some metals and their Poisson's Ratios.

The relative values between quantities - ratios and proportions.

Stress is force per unit area - strain is the deformation of a solid due to stress.

Young's Modulus (or Tensile Modulus alt. Modulus of Elasticity) and Ultimate Tensile Strength and Yield Strength for materials like steel, glass, wood and many more.

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