# In a uniaxial tensile test on a specimen of a ductile material, the ultimate tensile strength is found to be 400 MPa and the elongation up to the maxi

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In a uniaxial tensile test on a specimen of a ductile material, the ultimate tensile strength is found to be 400 MPa and the elongation up to the maximum load is 25%. The true stress at the maximum load in MPa is ______.

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Concept:

Engineering stress-strain is lower than true stress-strain because we consider the initial area only throughout the process while in true stress-strain curve we consider the instantaneous area.

Mathematically,

$\rm{Engineering~Stress}\;(σ_o)={Applied~Force\over Initial~Area}$

$\rm{True~Stress}\;(σ_t)={Applied~Force\over Instantaneous~Area}$

Mathematically, true stress (σT) and engineering stress (σo) relation is represented as

σt = σo(1 + ϵo)

ϵt = ln (1 + ϵo)

where σo = engineering stress, σt = true stress, and ϵo = engineering strain and ϵt = true strain.

Calculation:

Given:

ϵo = 0.25, σo = 400 MPa

We know that

σt = σo(1 + ϵo)

σ= 400(1 + 0.25)

σt = 500 MPa.