True Stress - True Strain

True Stress - True Strain
TECTechnics Classroom TECTechnics Overview

True Stress True Strain

(a) The conventional strain in a member subjected to a tensile stress of 14,815 psi is 0.350. Calculate the true stress and the true strain. Assuming constant volume.

(b) The original diameter of a tension specimen is 0.505 inches (figure 115.4). At a certain load, the diameter is found to be 0.388 inches. Calculate the true and conventional strain at this point. Assuming constant volume.

The strings: S₇P₃A₃₁ (Force - Pull).

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

True Stress True Strain

Formulas of interest:
Conventional (also called nominal, or engineering) stress, σ = Load/A_o
Where A_o is original cross-section area of member
Conventional(also called nominal, or engineering) strain, ε = δ/l_o
Where l₀ is original length of member
True stress, σ' = Load/A'
Where A' is actual area of the cross-section corresponding to the given load.
True (also called natural) strain, ε' = log_e(A_o/A') = log_e(1 + ε)

(a) σ = Load/A_o ; σ' = Load/A'
So, σ' = σ(A_o/A')
ε' = log_e(A_o/A') = log_e(1 + ε)
So, (A_o/A') = (1 + ε) = 1.350
So, σ' = 14,815(1.350) = 20,000 psi
So, true stress = 20,000 psi
ε' = log_e(1 + ε) = log_e(1.350) = 0.300
So, true strain = 0.300.

(b) A_o = π(0.505/2)².
A' = π(0.388/2)².
So, A_o/A' = 0.505²/0.388²
ε' = log_e(A_o/A') = log_e(1 + ε)
So, true strain, ε' = log_e((0.505²/0.388²) = 0.527.
So,conventional strain, ε = e^0.527 - 1 = 0.694.

Math

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