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)
σt = 400(1 + 0.25)
σt = 500 MPa.