MAT-36

Hollomon hardening

σ = K ε^n. Power-law true stress–strain in the plastic range.

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PlasticityHollomon 1945

Governing equation

\sigma=K\varepsilon^n

where

K: Strength coefficient (MPa)
\varepsilon: True strain (—)
n: Hardening n (—)
\sigma: True stress (MPa)

Lecture brief

Historical brief

Hooke (1678), Hall–Petch grain size, Arrhenius activation and Paris fatigue-crack growth are the spine of materials selection. The sheets relate stress, microstructure and life. This sheet (MAT-36 — Hollomon hardening) is the form associated with Hollomon 1945. Working symbols: $K$ , $\varepsilon$ , $n$ $\rightarrow$ $\sigma$ . Hollomon fitted the plastic branch of many metals to a power law. n is the strain-hardening exponent, K the strength coefficient.

Purpose

Purpose: compute

\sigma

from

K

\varepsilon

n

in Materials via

\sigma=K\varepsilon^n

σ = K ε^n. Power-law true stress–strain in the plastic range. Use it when a real materials question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

K = 800.000\,\mathrm{MPa}

\varepsilon = 0.080\,\mathrm{—}

n = 0.200\,\mathrm{—}

, the governing relation

\sigma=K\varepsilon^n

yields

\sigma = 482.7\,\mathrm{MPa}

. A log–log σ–ε line, an n slope. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Strength coefficient K800 MPaTrue strain \varepsilon0.08 —Hardening n n0.2 —

Outputs

True stress \sigma482.7 MPa

Reading speed

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Narration of this film

A log–log σ–ε line, an n slope.

Hollomon fitted the plastic branch of many metals to a power law. n is the strain-hardening exponent, K the strength coefficient.

Reading speed

Watch on YouTube