Question 1

What is the Ramberg-Osgood model and what is its equation?

Accepted Answer

The Ramberg-Osgood model is an empirical equation that describes the elastic-plastic stress-strain relationship of metals: ε = σ/E + (σ/K)^(1/n). The total strain ε is the sum of the elastic component σ/E and the plastic component (σ/K)^(1/n). K is the strength coefficient (MPa) and n is the strain hardening exponent (dimensionless). A small n means rapid hardening (typical for steel: 0.10–0.30), while a large n means gradual hardening (pure copper: 0.50–0.55).

Question 2

What is the difference between engineering stress and true stress?

Accepted Answer

Engineering stress is defined as σ_eng = F/A₀ (original cross-sectional area A₀), while true stress accounts for the current area: σ_true = F/A. The conversion relations are σ_true = σ_eng(1 + ε_eng) and ε_true = ln(1 + ε_eng). Before necking begins, the true stress-strain curve is monotonically increasing, whereas the engineering curve descends after UTS. FEM material cards (plasticity input) require true stress vs. true plastic strain data.

Question 3

How do you identify K and n from tensile test data?

Accepted Answer

Plot the plastic strain data (ε_p = ε_total − σ/E) on a log-log scale (log σ vs. log ε_p). The power law σ = K·ε_p^n produces a straight line; the slope gives n and the intercept gives log K (Hollomon plot). Because the Ramberg-Osgood form assumes continuous plastic strain from zero, it is especially well-suited for materials without a sharp yield point such as aluminium alloys. For FEM, create a table of true stress vs. true plastic strain starting at the yield stress.

Question 4

How is toughness calculated and what does it represent?

Accepted Answer

Toughness is the area under the engineering stress-strain curve and represents the energy absorbed per unit volume up to fracture (units: MJ/m³ = MPa). This tool computes it numerically using the trapezoidal rule. As an example, SS400 with E = 206 GPa, σY = 245 MPa, K = 530 MPa, n = 0.26, and εmax = 30% yields a toughness of roughly 110–130 MJ/m³. Toughness depends on both strength and ductility, so a high-strength low-elongation steel like HT980 can have similar or lower toughness than a milder steel.

Elastic-Plastic Stress-Strain
Curve Generator

Theory Note — Elastic-Plastic Constitutive Law

Elastic-Plastic Stress-StrainCurve Generator

Theory Note — Elastic-Plastic Constitutive Law

Elastic-Plastic Stress-Strain
Curve Generator