MAT-31

Linear thermal expansion

ΔL = α L ΔT. Length change from a temperature step.

Reading speed

ElasticityISO 11359

Governing equation

\Delta L=\alpha L\Delta T

where

\alpha: CTE (10^{-6}/K)
L: Length (m)
\Delta T: Temperature rise (K)
\Delta L: Extension (mm)

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-31 — Linear thermal expansion) is the form associated with ISO 11359. Working symbols: $\alpha$ , $L$ , $\Delta T$ $\rightarrow$ $\Delta L$ . The linear CTE α is (1/L) dL/dT. Integrated at constant α it is ΔL/L = α ΔT, the origin of thermal stress E α ΔT.

Purpose

Purpose: compute

\Delta L

from

\alpha

L

\Delta T

in Materials via

\Delta L=\alpha L\Delta T

ΔL = α L ΔT. Length change from a temperature step. Use it when a real materials question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

\alpha = 12.000\,\mathrm{10^-6/K}

L = 2.000\,\mathrm{m}

\Delta T = 80.000\,\mathrm{K}

, the governing relation

\Delta L=\alpha L\Delta T

yields

\Delta L = 1.920\,\mathrm{mm}

. A bar, a thermometer, a stretch. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

CTE \alpha12 10^{-6}/KLength L2 mTemperature rise \Delta T80 K

Outputs

Extension \Delta L1.920 mm

Reading speed

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Narration of this film

A bar, a thermometer, a stretch.

The linear CTE α is (1/L) dL/dT. Integrated at constant α it is ΔL/L = α ΔT, the origin of thermal stress E α ΔT.

Reading speed

Watch on YouTube