Young's modulus (or Modulus of elasticity) is the measure of rigidity or stiffness of a material; the ratio of stress to the corresponding strain below the proportional limit. The modulus of elasticity is the slope of the stress-strain curve in the range of linear proportionality of stress to strain in the stress-strain curve.
For most metals that are stressed in tension and at relatively low levels, stress and strain are proportional to each other through the relationship σ= Eε.
The constant of proportionality E (GPa or psi) is the modulus of elasticity, or Young’s modulus.
Here σ is engineering stress and ε is engineering strain.
The units of engineering stress are megapascals, MPa (SI) (where 1 MPa N/m2 ), and pounds force per square inch, psi (Customary U.S.). Engineering strain is unitless.
Young's modulus of steel at room temperature is typically between 190 GPa (27500 ksi) and 215 GPa (31200 ksi). Young's modulus of carbon steels (mild, medium and high), alloy steels, stainless steels and tool steels are given in the following table in GPA and ksi.
^{Ref-1} Elastic modulus of carbon and low-alloy cast steels at room temperature are only slightly affected by changes in composition and structure. The modulus of elasticity, E, is about 200 GPa (29 × 10^{6} psi). Increasing temperature has a effect on the modulus of elasticity.
A typical value of the modulus of elasticity:
- at 200 °C (400 °F) is about 193 GPa (28 × 10^{6} psi);
- at 360 °C (680 °F), 179 GPa (26 × 10^{6} psi);
- at 445 °C (830 °F), 165 GPa (24 × 10^{6} psi);
- and at 490 °C (910 °F), 152 GPa (22 × 10^{6} psi).
- Above 480 °C (900 °F), the value of the modulus of elasticity decreases rapidly.
^{Ref-1} For all practical purposes, modulus of elasticity of all tool steels in all conditions is about 210 GPa (30 × 10^{6} psi) at room temperature. Elastic modulus decreases uniformly to about 185 GPa (27 × 10^{6} psi) at 260 °C (500 °F) and about 150 GPa (22 × 10^{6} psi) at 540 °C (1000 °F).