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Mechanical properties and fracture

In a tensile test, the engineering stress was 400 MPa at an engineering strain of 0.20, before necking began. Assuming constant volume during plastic deformation, which value is closest to the true stress at this point?

  1. AAbout 333 MPa
  2. BAbout 400 MPa
  3. CAbout 480 MPa
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Answer: C. About 480 MPa

Constant volume gives A₀L₀ = AL, so A = A₀/(1 + e), and the true stress is σ_T = σ(1 + e) = 400 × 1.20 = 480 MPa. The true strain at this point is ε_T = ln(1 + e) = ln 1.20 ≈ 0.182. About 333 MPa divides by (1 + e) where it should multiply; as the cross section shrinks, the actual stress becomes larger than the engineering stress. About 400 MPa is just the engineering stress, ignoring the reduction in area. This conversion is valid only up to the onset of necking, while deformation is uniform throughout the specimen.

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