True Stress-Strain Calculator

True Stress-Strain Formula

Worked Example

A tensile test reading 400 MPa at 20 % engineering strain:

1. σ_T = σ_e(1 + ε_e) = 400 × 1.2 = 480 MPa
2. ε_T = ln(1 + ε_e) = ln(1.2) = 0.1823215568

Necking starts when ε_T = n: 0.2 · Valid until: the onset of necking (uniform deformation)

GATE tip

Considère’s criterion: necking begins when dσ_T/dε_T = σ_T, which for the Hollomon law gives ε_T = n; the ultimate tensile strength is then K nⁿ e^(−n).

More Mechanical Behaviour Calculators

• Fracture Toughness Calculator

  K_I = Y σ √(πa)

  fracture when K_I ≥ K_Ic; a edge crack length or half an internal crack

  Example: A 2 mm edge crack (Y = 1.12) under 300 MPa: Stress intensity K_I = 26.6336 MPa·√m.

  Open the fracture toughness calculator →

• Paris Law Calculator

  da/dN = C (ΔK)^m, ΔK = YΔσ√(πa)

  N = [a_f^(1−m/2) − a₀^(1−m/2)] / [C(YΔσ√π)^m (1 − m/2)] for m ≠ 2

  Example: A crack growing from 1 mm to 10 mm under a 150 MPa stress range, C = 10⁻¹¹, m = 3, Y = 1.12: Cycles to grow the crack N_f = 163791.

  Open the paris law calculator →

• Larson-Miller Parameter Calculator

  LMP = T (C + log₁₀ t_r)

  T in kelvin, t_r in hours, C ≈ 20 for many alloys

  Example: An alloy that ruptures in 1000 h at 650 °C, raised to 700 °C at the same stress: Rupture time t₂ = 65.8068 h.

  Open the larson-miller parameter calculator →

Frequently asked questions

Sources

• The International System of Units (SI), 9th edition (SI Brochure), Bureau International des Poids et Mesures .

Last reviewed: 2026-10-15. Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.