Modulus Of Elasticity Rubber
The modulus of elasticity describes the relationship between the stress applied to a material and its corresponding strain. Stress is defined as a force applied over a unit area, with typical units of pounds per square inch (psi) or Newtons per square meter — also known as pascals (Pa). Strain is a measure of the amount that a material deforms when stress is applied and is calculated by measuring the amount of deformation when under stress, as compared to the matter's original dimensions. Modulus of elasticity is based on Hooke’s Law of elasticity and can be calculated by dividing the stress by the strain.
For many materials at low levels of stress and under tension, the stress and strain are proportional — meaning they increase and decrease in a constant way, relative to each other. Deformation of a material that occurs when the stress and strain behave proportionally is known as elastic deformation or elastic strain. Modulus of elasticity describes the relationship between stress and strain when under these conditions.
The Young's Modulus of a material is a fundamental property of every material that cannot be changed. It is dependent upon temperature and pressure however. The Young's Modulus (or Elastic Modulus) is in essence the stiffness of a material. In other words, it is how easily it is bended or stretched. The modulus of elasticity (also known as the elastic modulus, the tensile modulus, or Young's modulus) defined as the slope of its stress–strain curve in the elastic deformation region. Where stress is the force causing the deformation divided by the area to which the force is applied and strain is the ratio of the change in some length parameter caused by the deformation to the original value of the length parameter. Young's modulus (E) describes tensile elasticity, or the tendency of an object to deform along an axis when opposing forces are applied along that axis; it is defined as the ratio of tensile stress to tensile strain. It is often referred to simply as the elastic modulus.
Elasticity is the ability of a material to return to its original state or dimensions after a load, or stress, is removed. Elastic strain is reversible, meaning the strain will disappear after the stress is removed and the material will return to its original state. Materials that are exposed to intense levels of stress may deform to the point where the stress and strain no longer behave proportionally, and the material will not return to its original dimensions. This is referred to as plastic deformation or plastic strain.
Stress is force per unit area - strain is the deformation of a solid due to stress
Modulus Of Elasticity Of Tire Rubber
Stress
Stress is the ratio of applied force F to a cross section area- defined as 'force per unit area'.
- tensile stress - stress that tends to stretch or lengthen the material - acts normal to the stressed area
- compressive stress - stress that tends to compress or shorten the material - acts normal to the stressed area
- shearing stress - stress that tends to shear the material - acts in plane to the stressed area at right-angles to compressive or tensile stress
Tensile or Compressive Stress - Normal Stress
Tensile or compressive stress normal to the plane is usually denoted 'normal stress' or 'direct stress' and can be expressed as
σ = Fn/ A (1)
where
σ = normal stress (Pa (N/m2), psi (lbf/in2))
Fn = normal force acting perpendicular to the area (N, lbf)
A = area (m2, in2)
- a kip is an imperial unit of force - it equals 1000 lbf (pounds-force)
- 1 kip = 4448.2216 Newtons (N) = 4.4482216 kilo Newtons (kN)
A normal force acts perpendicular to area and is developed whenever external loads tends to push or pull the two segments of a body.
Example - Tensile Force acting on a Rod
A force of 10 kN is acting on a circular rod with diameter 10 mm. The stress in the rod can be calculated as
σ = (10 103 N)/ (π ((10 10-3 m) / 2)2)
= 127388535 (N/m2)
= 127 (MPa)
Example - Force acting on a Douglas Fir Square Post
A compressive load of 30000 lb is acting on short square 6 x 6 in post of Douglas fir. The dressed size of the post is 5.5 x 5.5 in and the compressive stress can be calculated as
σ = (30000 lb)/ ((5.5 in) (5.5 in))
= 991 (lb/in2, psi)
Shear Stress
Stress parallel to a plane is usually denoted as 'shear stress' and can be expressed as
τ = Fp/ A (2)
where
τ = shear stress (Pa (N/m2), psi (lbf/in2))
Fp = shear force in the plane of the area (N, lbf)
A = area (m2, in2)
A shear force lies in the plane of an area and is developed when external loads tend to cause the two segments of a body to slide over one another.
Strain (Deformation)
Strain is defined as 'deformation of a solid due to stress'.
- Normal strain - elongation or contraction of a line segment
- Shear strain - change in angle between two line segments originally perpendicular
Normal strain and can be expressed as
ε = dl / lo
= σ / E (3)
Modulus Of Elasticity Rubber
where
dl = change of length (m, in)
lo = initial length (m, in)
ε = strain - unit-less
E = Young's modulus (Modulus of Elasticity) (Pa , (N/m2), psi (lbf/in2))
- Young's modulus can be used to predict the elongation or compression of an object when exposed to a force
Note that strain is a dimensionless unit since it is the ratio of two lengths. But it also common practice to state it as the ratio of two length units - like m/m or in/in.
- Poisson's ratio is the ratio of relative contraction strain
Example - Stress and Change of Length
The rod in the example above is 2 m long and made of steel with Modulus of Elasticity200 GPa (200 109 N/m2). The change of length can be calculated by transforming (3) to
dl = σ lo / E
= (127 106 Pa) (2 m) / (200 109 Pa)
= 0.00127 m
= 1.27 mm
Strain Energy
Stressing an object stores energy in it. For an axial load the energy stored can be expressed as
U = 1/2 Fn dl
where
U = deformation energy (J (N m), ft lb)
Young's Modulus - Modulus of Elasticity (or Tensile Modulus) - Hooke's Law
Most metals deforms proportional to imposed load over a range of loads. Stress is proportional to load and strain is proportional to deformation as expressed with Hooke's Law.
E = stress / strain
= σ/ ε
= (Fn / A) / (dl / lo) (4)
where
E = Young's Modulus (N/m2) (lb/in2, psi)
Modulus of Elasticity, or Young's Modulus, is commonly used for metals and metal alloys and expressed in terms 106 lbf/in2, N/m2 or Pa. Tensile modulus is often used for plastics and is expressed in terms 105 lbf/in2 or GPa.
Shear Modulus of Elasticity - or Modulus of Rigidity
G = stress / strain
= τ / γ
= (Fp / A) / (s / d) (5)
where
G = Shear Modulus of Elasticity - or Modulus of Rigidity (N/m2) (lb/in2, psi)
τ = shear stress ((Pa) N/m2, psi)
γ = unit less measure of shear strain
Fp = force parallel to the faces which they act
A = area (m2, in2)
s = displacement of the faces (m, in)
d = distance between the faces displaced (m, in)
Bulk Modulus Elasticity
The Bulk Modulus Elasticity - or Volume Modulus - is a measure of the substance's resistance to uniform compression. Bulk Modulus of Elasticity is the ratio of stress to change in volume of a material subjected to axial loading.
Elastic Moduli
Elastic moduli for some common materials:
| Material | Young's Modulus - E - | Shear Modulus - G - | Bulk Modulus - K - | |||
|---|---|---|---|---|---|---|
| GPa | 106 psi | GPa | 106psi | GPa | 106psi | |
| Aluminum | 70 | 10 | 24 | 3.4 | 70 | 10 |
| Brass | 91 | 13 | 36 | 5.1 | 61 | 8.5 |
| Copper | 110 | 16 | 42 | 6.0 | 140 | 20 |
| Glass | 55 | 7.8 | 23 | 3.3 | 37 | 5.2 |
| Iron | 91 | 13 | 70 | 10 | 100 | 14 |
| Lead | 16 | 2.3 | 5.6 | 0.8 | 7.7 | 1.1 |
| Steel | 200 | 29 | 84 | 12 | 160 | 23 |
- 1 GPa = 109 Pa (N/m2)
Related Topics
- Mechanics - Forces, acceleration, displacement, vectors, motion, momentum, energy of objects and more
- Statics - Loads - force and torque, beams and columns
Latex Rubber Modulus Of Elasticity
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