Structural components subjected to large contact forces (e.g., brake disks) are often made...

Structural components subjected to large contact forces (e.g., brake disks) are often made of high-grade steel coated with a thin film of a very hard material such as diamond. A common test to assess the mechanical properties (hardness, elastic moduli, etc.) of the coating is the nanoindentation test, which, roughly speaking, consists of making a controlled dent in the film using a nail-like object, called an indentor. During the test one measures the force applied to the indentor and the indentation depth. In the graph shown, you can see the curves interpolating the loading and unloading data for a diamond film on steel. Since the unloading curve does not go back to the origin of the plot, the film is permanently deformed during the indentation process (i.e., an actual permanent dent remains). Determine the energy lost to permanent deformation if the indentation force is given by

where FI is expressed in μN and x (indentation depth) in nm.

Figure P4.14