Notes on Metal

Presentation

When looking for a rigid substance, metal is a good choice compare to stone, wood, glass, ceramic, plastic. The rigidity is relevant when designing parts with the solid mechanics. In this matter, shapes and dimensions are considered invariant, regardless of the strength, pressure, collision and temperature conditions.

Metal overview

Rigidity

Material Young’s modulus Yield stress Yield strain Thermal expansion
Units GPa MPa % 10**-6/°C
Iron (Fe) 196 80 0.04 11.8
cast iron 83 400 0.4 10.5
Steel 204 1450 0.7 17
Aluminium (Al) 69 95 0.13 23.1
Aluminium alloy 75 470 0.64  
Copper (Cu) 124 33 0.03 17
Zinc (Zn) 78      

Example of thermal expansion:

An iron-part with a width of 10 cm gets longer of 11.8 um when the temperature increases of 10 °C.

Example of limit of elasticity:

An iron-part under strength with a width of 10 cm gets longer of 200 um before getting a plastic deformation.

Auxiliary

Material Molar mass Specific volume Specific heat Thermal conductivity Electrical resistivity
Units kg/mol m3/kg J/(kg.K) W/(m.K) Ohm.m
Iron (Fe) 0.05584 127.0 * 10**-6 444 80.4 9.70 * 10**-8
Aluminium (Al) 0.02698 370.4 * 10**-6 897 237 2.65 * 10**-8
Copper (Cu) 0.06354 111.6 * 10**-6 385 384.1 1.68 * 10**-8
Zinc (Zn) 0.06539 140.0 * 10**-6 380 116 5.90 * 10**-8

Energy for fusion

_images/heat_temperature_diagram.png

At 101325 Pa (normal atmospheric pressure)

Material Cp [solid] Fusion Tc Fusion heat Cp [liquid] Boiling Tc Vaporization heat Cp [gaz]
Units J/(kg.K) °C J/kg J/(kg.K) °C J/kg J/(kg.K)
Water (H2O) 2108 0 334000 4187 100 2264705 1996
Nitrogen (N2)   -210 25700   -196 200000 1025
Iron (Fe) 444 1538 247134 820 2861 6214000  
Aluminium (Al) 897 660.3 396590 1180 2519 10859000  
Copper (Cu) 385 1084.6 206170 490 2562 4721000  
Zinc (Zn) 380 419.5 112402   907 1819000  
_images/heat_temperature_T0.png _images/heat_temperature_T-100.png

Energy to melt 1 kg of metal:

Water-steam   :  100 * 4187 + 2264705 = 2683405 J  <=> 0.745 kW/h
Iron          : 1538 *  444 +  247134 =  930006 J  <=> 0.258 kW/h
Aluminium     :  669 *  897 +  396590 =  996683 J  <=> 0.276 kW/h
Copper        : 1084 *  385 +  206170 =  623510 J  <=> 0.173 kW/h
Zinc          :  419 *  380 +  112402 =  271622 J  <=> 0.075 kW/h

Reminder:

\[1 bar = 100000 Pa\]
\[1 Pa = 1 Nm^{-2} = 1 J m^{-3}\]
\[1 cal = 4.1855 J\]
\[1 mol = 6.022 * 10^{23}\]

Auxiliary table

Material Molar mass Specific volume Thermal conductivity Electrical resistivity Magnetic permeability
Units kg/mol m3/kg W/(m.K) Ohm.m H/m
Ice (H2O) 0.018 0.00109      
Water (H2O) 0.018 0.00100 0.6 20 0.99
Steam (H2O) 0.018 1.24      
Nitrogen (N2) 0.02802 0.799 0.026 10**9 1.00
Iron (Fe) 0.05584 127.0 * 10**-6 80.4 9.70 * 10**-8 5000
Aluminium (Al) 0.02698 370.4 * 10**-6 237 2.65 * 10**-8 1.00
Copper (Cu) 0.06354 111.6 * 10**-6 384.1 1.68 * 10**-8 0.99
Zinc (Zn) 0.06539 140.0 * 10**-6 116 5.90 * 10**-8 0.99