Density Density is defined as mass per unit volume; it is a measure of how compact the mate-
rial is for a given volume. For example, the average density of aluminum alloys is 2700 kg /m
3and compared to steel density of 7850 kg/m
3
, aluminum has a density that is approximately one-
third the density of steel.Modulus of Elasticity (Young’s Modulus) Modulus of elasticity is a measure of how easily a mate-
rial will stretch when pulled (subject to a tensile force) or how well the material will shorten
when pushed (subject to a compressive force). The larger the value of the modulus of elasticity
is, the larger the required force would be to stretch or shorten the material. For example, the
modulus of elasticity of aluminum alloy is in the range of 70 to 79 GPa, whereas steel has a mod-
ulus of elasticity in the range of 190 to 210 GPa; therefore, steel is approximately 3 times stiffer
than aluminum alloys.Modulus of Rigidity (Shear Modulus) Modulus of rigidity is a measure of how easily a material
can be twisted or sheared. The value of modulus of rigidity, also calledshear modulus, shows the
resistance of a given material to shear deformation. Engineers consider the value of shear mod-
ulus when selecting materials for shafts and rods that are subjected to twisting torques. For
example, the modulus of rigidity or shear modulus for aluminum alloys is in the range of 26 to
36 GPa, whereas the shear modulus for steel is in the range of 75 to 80 GPa. Therefore, steel
is approximately three times more rigid in shear than aluminum.Tensile Strength The tensile strength of a piece of material is determined by measuring the
maximum tensile load a material specimen in the shape of a rectangular bar or cylinder can
carry without failure. The tensile strength or ultimate strength of a material is expressed as the
maximum tensile force per unit cross-sectional area of the specimen. When a material specimen
is tested for its strength, the applied tensile load is increased slowly. In the very beginning of the
test, the material will deform elastically, meaning that if the load is removed, the material will
return to its original size and shape without any permanent deformation. The point to which
the material exhibits this elastic behavior is calledyield point. The yield strength represents the
maximum load that the material can carry without any permanent deformation. In certain engi-
neering design applications (especially involving brittle materials), the yield strength is used as
the tensile strength.Compression Strength Some materials are stronger in compression than they are in tension;
concrete is a good example. The compression strength of a piece of material is determined by
measuring the maximum compressive load a material specimen in the shape of cylinder or cube
can carry without failure. The ultimate compressive strength of a material is expressed as the
maximum compressive force per unit cross-sectional area of the specimen. Concrete has a com-
pressive strength in the range of 10 to 70 MPa.Modulus of Resilience Modulus of resilience is a mechanical property of a material that shows
how effective the material is in absorbing mechanical energy without sustaining any perma-
nent damage.556 Chapter 17 Engineering Materials
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