MAT-40

Considère necking

Necking when n equals true strain for Hollomon.

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GoverningConsidère necking

Governing equation

\sigma_t=d\sigma_t/d\varepsilon_t

$n \in \left[0.05, 0.5\right]$

where

K: K (MPa)
n: n (—)
en: Considère necking (—)

The figure, part by part

Each numbered marker wears the color of its card. Hover a card to light the marker. Tap a marker to jump to that card. The slider walks a red point along the curve; Animate drawing traces it like a pen.

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①

Governing law — red

\sigma_t=d\sigma_t/d\varepsilon_t

$n \in \left[0.05, 0.5\right]$

$n = 0.05$ $en = 0.05$

Along the curve

②

Domain of the variable — blue

n_{\min} = 0.05,\quad n_{\max} = 0.5

$n \in \left[0.05, 0.5\right]$

$n = 0.05$ $n = 0.05$

Along the curve

③

Response curve — green

\sigma_t=d\sigma_t/d\varepsilon_t

$n \in \left[0.05, 0.5\right]$

$n = 0.05$ $en = 0.05$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}en}{\mathrm{d}n}

$n \in \left[0.05, 0.5\right]$

$n = 0.053$ $en^{\prime} = 1$

Along the curve

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-40 — Considère necking) is the form associated with Considère necking. Working symbols: $K$ , $n$ $\rightarrow$ $en$ . Necking when n equals true strain for Hollomon. Pedagogical SI sheet with a live model and a swept parameter.

Purpose

Purpose: compute

en

from

K

n

in Materials via

\sigma_t=d\sigma_t/d\varepsilon_t

Necking when n equals true strain for Hollomon. 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 = 600.000\,\mathrm{MPa}

n = 0.200\,\mathrm{—}

, the governing relation

\sigma_t=d\sigma_t/d\varepsilon_t

yields

en = 0.200\,\mathrm{—}

. One governing identity, SI units, a single sweep on the sheet. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

K K600 MPan n0.2 —

Outputs

Considère necking en0.200 —

Reading speed

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Narration of this film

One governing identity, SI units, a single sweep on the sheet.

Necking when n equals true strain for Hollomon. Pedagogical SI sheet with a live model and a swept parameter.

Reading speed

Watch on YouTube