The engineering stress-strain curve is the fundamental characterisation of a material’s mechanical response to uniaxial loading. This calculator converts between engineering and true stress-strain, calculates work hardening exponent (n) and strength coefficient (K) from the Hollomon power law, and estimates key derived properties including resilience, toughness, and uniform elongation. Understanding these relationships is essential for metal forming analysis, finite element material model definition, and structural integrity assessment.

Stress-Strain Curve Parameters Calculator







Elastic strain at yield (ε_y = σ_y / E)
True stress at UTS (σ_T = UTS × (1 + ε_UTS))
True strain at UTS (ε_T = ln(1 + ε_UTS))
Work hardening exponent — n (Hollomon)
Strength coefficient — K (Hollomon: σ_T = K × ε_T^n)
Engineering stress at input strain
True stress at input strain
Modulus of resilience (U_r = σ_y² / 2E)
Toughness estimate (area under curve, MJ/m³)

Engineering stress: σ_e = F/A₀ | True stress: σ_T = σ_e × (1 + ε_e)
Engineering strain: ε_e = ΔL/L₀ | True strain: ε_T = ln(1 + ε_e)
Hollomon power law: σ_T = K × ε_T^n (valid in uniform plastic deformation region)
n = strain hardening exponent: high n = better formability (304 SS n≈0.45; mild steel n≈0.20)

Engineering Stress-Strain Curve — Key Points Labelled Engineering Strain (ε) Stress (σ) σ_y (Yield Strength) UTS (Ultimate Tensile Strength) Fracture σ_y UTS E = σ/ε Elastic Plastic (work hardening) Necking 0.2% offset © metallurgyzone.com/ — Tensile Testing Guide
Figure: Engineering stress-strain curve with all key points labelled: elastic modulus E (slope), yield strength σ_y (0.2% offset), UTS (peak), necking, and fracture. © metallurgyzone.com/

Typical Hollomon n Values for Engineering Alloys

Material n (strain hardening exponent) σ_y (MPa) Formability
304 Austenitic stainless 0.40–0.50 210–250 Excellent — very high n
IF (interstitial-free) steel 0.25–0.35 140–180 Excellent — deep draw quality
Low carbon mild steel (DC04) 0.20–0.25 180–240 Good — standard pressings
DP600 dual-phase steel 0.15–0.22 350–400 Good — AHSS auto panels
S355 structural steel 0.15–0.20 355–400 Moderate
S690 Q&T structural 0.05–0.10 690–750 Low — limited cold forming
Ti-6Al-4V (annealed) 0.08–0.12 880–950 Low — springback issues
Al 6061-T6 0.06–0.10 276–310 Low — limited forming after T6
Cu (annealed) 0.30–0.40 70–100 Excellent

References

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