Engineers and scientists often use units gigapascals or newtons per square millimeter to describe the strength and elasticity of materials. Yield stress, the force it takes to permanently bend a material, measures one type of material strength. It typically has units of N/mm^2, sometimes called MPa. Young's modulus measures elasticity, the amount of force a material can take before it breaks or becomes permanently bent, and has units of gigapascals, or GPa. A material with high elasticity usually has a high yield stress. Because they represent related material properties, learn to convert between GPa and N/mm^2.
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Set up a unit conversion between GPa and N/mm^2. There are 1,000 MPa in 1 GPa and 1 N/mm^2 per MPa, so for 3 GPa, for example, the conversion is (3 GPa)*(1,000 MPa/GPa)*(1 N/mm^2/MPa).
Multiply out the numbers and the units in the unit conversion. For example, (3 GPa)*(1,000 MPa/GPa)*(1 N/mm^2/MPa) = 3,000 GPa*MPa*N/GPa*MPa*mm^2.
Cancel like units out of the numerator and denominator. In 3,000 GPa*MPa*N/GPa*Mpa*mm^2, for example, GPa and MPa cancel, leaving 3,000 N/mm^2. Therefore, 3 GPa = 3,000 N/mm^2.
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- Divide by 1,000 to convert from N/mm^2 to GPa.
- One GPa equals 1 kN/mm^2, so (1 GPa)*(1 kN/mm^2/GPa)*[(1,000 N/mm^2/kN/mm^2)] is an alternate unit conversion.