Modulus of Elasticity

Modulus of elasticity. Rate of change of strain as a function of stress. The slope of the straight line portion of a stress-strain diagram. Tangent modulus of elasticity is the slope of the stress-strain diagram at any point. Secant modulus of elasticity is stress divided by strain at any given value of stress or strain. It also is called stress strain ratio. Tangent and secant modulus of elasticity are equal up to the proportional limit of a material.

Depending on the type of loading represented by the stress-strain diagram, modulus of elasticity may be reported as compressive modulus of elasticity (or modulus of elasticity in compression), flexural modulus of elasticity (or modulus of elasticity in flexure), shear modulus of elasticity (or modulus of elasticity in shear), tensile modulus of elasticity (or modulus of elasticity in tension) or torsional modulus of elasticity (or modulus of elasticity in torsion). Modulus of elasticity may be determined by dynamic mechanical testing where it can be derived from complex modulus.

Modulus used alone generally refers to tensile modulus of elasticity. Shear modulus is almost always equal to torsional modulus and both are called modulus of rigidity. Moduli of elasticity in tension and compression are approximately equal and are known as Young's modulus. Modulus of rigidity is related to Young's modulus by the equation: E = 2G (1 + r) where E is Young's modulus (psi), G is modulus of rigidity (psi) and r is Poisson's ratio. Modulus of elasticity also is called elastic modulus and coefficient of elasticity.

 The elastic modulus of an object is defined as the slope of its stress-strain curve in the elastic deformation region:

where λ (lambda) is the elastic modulus; 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 caused by the stress to the original state of the object. If stress is measured in pascals, since strain is a unitless ratio, then the units of λ are pascals as well. An alternative definition is that the elastic modulus is the stress required to cause a sample of the material to double in length. This is not realistic for most materials because the value is far greater than the yield stress of the material or the point where elongation becomes nonlinear, but some may find this definition more intuitive.
Specifying how stress and strain are to be measured, including directions, allows for many types of elastic moduli to be defined. The three primary ones are:

• 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.
• The shear modulus or modulus of rigidity (G or ) describes an object's tendency to shear (the deformation of shape at constant volume) when acted upon by opposing forces; it is defined as shear stress over shear strain. The shear modulus is part of the derivation of viscosity.
• The bulk modulus (K) describes volumetric elasticity, or the tendency of an object to deform in all directions when uniformly loaded in all directions; it is defined as volumetric stress over volumetric strain, and is the inverse of compressibility. The bulk modulus is an extension of Young's modulus to three dimensions.

References -

Tinius Olsen Knowledge Centre - http://tiniusolsen.com/resource-center/mechanical-properties-m.html

Wikipedia - http://en.wikipedia.org/wiki/Elastic_modulus

For information please contact -

Amit Mitbawkar
Team Leader - Industrial Materials Testing
SIGMA ENTERPRISES LLC
Engineering Products Division
PO Box - 96241,
Dubai, UAE
Tel - +971 4 8851828
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Email – amit_mitbawkar@sep.ae
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