Elastic Strain - Plastic Strain

Elastic Strain - Plastic Strain
TECTechnics Classroom TECTechnics Overview

Elastic Strain - Plastic Strain

The proportional limit of a member made of a type of steel is 30,000 psi. Modulus of elasticity of member is 30 x 10⁶ psi. When this member is subjected to a tensile load of 45,000 psi, the strain is 0.0615 in./in. When this member is subjected to a tensile load of 60,000 psi, the strain is 0.2020 in./in.

What is the ratio of elastic strain to plastic strain?

The strings: S₇P₃A₃₁ (Force - Pull).

The math:
Pj Problem of Interest is of type force (pull).

Elastic-Strain-Plastic-Strain

Formula of interest:
Stress = (modulus of elasticity)(strain)
Strain = Stress/Modulus of Elasticity

The plastic range in a stress-strain relationship is the region in which yielding and strain-hardening takes place. The strain from this yielding is permanent.

Load = 30,000 psi:
Elastic strain, ε_e = 30,000/(30 x 10⁶) = 0.0010 in./in.
No plastic strain since this is the proportional limit stress.

Load = 45,000 psi:
Elastic strain, ε_e = 45,000/(30 x 10⁶) = 0.0015 in./in
plastic strain, ε_p = 0.0615 - 0.0015 = 0.0600 in./in.
So, ε_e/ε_p = 1/40
So, ε_e = 2.5% of ε_p

Load = 60,000 psi:
Elastic strain, ε_e = 60,000/(30 x 10⁶) = 0.0020 in./in
plastic strain, ε_p = 0.2020 - 0.0020 = 0.2000 in./in.
So, ε_e/ε_p = 1/100
So, ε_e = 1% of ε_p

Math

The point . is a mathematical abstraction. It has negligible size and a great sense of position. Consequently, it is front and center in abstract existential reasoning.
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