MAT-37

Larson–Miller parameter

P = T (C + log10 tr) / 1000. Time–temperature collapse of rupture data.

Reading speed

CreepLarson–Miller 1952

Governing equation

P=T(C+\log_{10} t_r)/1000

$T \in \left[500, 1400\right]$

where

T: Temperature (K)
C: Larson–Miller C (—)
t_r: Rupture time (h)
P: LMP / 1000 (—)

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.

00:0 / 00:08

①

Governing law — red

P=T(C+\log_{10} t_r)/1000

$T \in \left[500, 1400\right]$

$T = 500$ $P = 11.5$

Along the curve

②

Domain of the variable — blue

T_{\min} = 500,\quad T_{\max} = 1400

$T \in \left[500, 1400\right]$

$T = 500$ $T = 500$

Along the curve

③

Response curve — green

P=T(C+\log_{10} t_r)/1000

$T \in \left[500, 1400\right]$

$T = 500$ $P = 11.5$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}P}{\mathrm{d}T}

$T \in \left[500, 1400\right]$

$T = 505.7$ $P^{\prime} = 0.023$

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-37 — Larson–Miller parameter) is the form associated with Larson–Miller 1952. Working symbols: $T$ , $C$ , $t_r$ $\rightarrow$ $P$ . Arrhenius inversion: a higher T for a shorter time is equivalent to a lower T for a longer time. C ≈ 20 for steels.

Purpose

Purpose: compute

P

from

T

C

t_r

in Materials via

P=T(C+\log_{10} t_r)/1000

P = T (C + log10 tr) / 1000. Time–temperature collapse of rupture data. Use it when a real materials question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

T = 900.000\,\mathrm{K}

C = 20.000\,\mathrm{—}

t_r = 1000.000\,\mathrm{h}

, the governing relation

P=T(C+\log_{10} t_r)/1000

yields

P = 20.70\,\mathrm{—}

. A master curve, a T–t pair, a P tick. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Temperature T900 KLarson–Miller C C20 —Rupture time t_r1000 h

Outputs

LMP / 1000 P20.70 —

Reading speed

Watch on YouTube

Free library

Full library

Free PDF / open book

YouTube channels

00:0 / 00:08

Narration of this film

A master curve, a T–t pair, a P tick.

Arrhenius inversion: a higher T for a shorter time is equivalent to a lower T for a longer time. C ≈ 20 for steels.

Reading speed

Watch on YouTube