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Strain
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Strain, true stress and strain

Indira Roy
GATE AIR 395 || Passionate about teaching

1. STRAIN

2. Tensile strain (Et) Compressive strain EC Shear strain (Y)

3. . Strain (e): The displacement per unit length (dimensionless) is known as strain. Tensile strain (Et) The elongation per unit length as shown in the figure is known as tensile strain. It is engineering strain or conventional strain. Here we divide the elongation to original length not actual length (Lo + L) Lo

4. Compressive strain (Ec: If the applied force is compressive then the reduction of length per unit length is known as compressive strain. . It is negative. Then cAL)/ Lo Shear Strain ( ): . When a force P is applied tangentially to the element shown. Its edge displaced to dotted line. . where is the lateral displacement of the upper face of the element relative to the lower face and L is the distance between these faces. Then the shear strain is Y = / L

5. TRUE STRESS AND TRUE STRAIN TRUE STRESS: The true stress is defined as the ratio of the load to the cross section area at any instant. load instantaneous area . where and is the engineering stress and engineering strain respectively.

6. TRUE STRAIN: Engineering strain: =e4-1 The volume of the specimen is assumed to be constant during plastic deformation. [ Ao AL ] It is valid till the neck formation.

7. Comparison Of Engineering And The True Stress- strain Curves The true stress-strain curve is also known as the flow curve True Stress-Strain Curve True stress-strain curve gives a true indication of deformation characteristics because it is based on the instantaneous dimension of the specimen. True Stress-Strain Curve Corrected for oomplex stress state in the neck region Engineering Stress-Strain Curve In engineering stress-strain curve, stress drops down after necking since it is based on the original area. Onset of necking In true stress-strain curve, the stress however increases after necking since the crosssectional area of the specimen decreases rapidly after necking.

8. The flow curve of many metals in the region of uniform plastic deformation can be expressed by the simple power law Where K is the strength coefficient n is the strain hardening exponent . n 0 perfectly plastic solid n 1 elastic solid For most metals, 0.1< n <0.5

9. Relation Between The Ultimate Tensile Strength And True Stress At Maximum Load %) = ha! Ao . The ultimate tensile strength: ( . The true stress at maximum load ((o,1))T- Ao Lo 0

10. . And true strain at maximum load oreet . Eliminating Prax we get, ( ),-max . Where Pmax = maximum force and Ao Original cross section areda PrnaxxAg ue4 0 A Instantaneous cross section ared