Most material properties are reported without specifying crystal directions because, in many practical applications, materials behave isotropically, especially when considering polycrystalline structures where grains are randomly oriented. For instance, the bulk stiffness of polycrystalline iron averages around 210 GPa, despite individual grains exhibiting varying stiffness based on their crystallographic orientation. However, in certain applications, such as single-crystal turbine blades, crystal orientation can significantly impact performance. Amorphous materials, lacking a defined crystal structure, further support the notion of isotropy. Overall, while some materials exhibit directional properties, many common applications can rely on averaged isotropic values.
