Indentation hardness

Indentation hardness tests are used in mechanical engineering to determine the hardness of a material to deformation. Several such tests exist, wherein the examined material is indented until an impression is formed; these tests can be performed on a macroscopic or microscopic scale.

When testing metals, indentation hardness correlates roughly linearly with tensile strength, but it is an imperfect correlation often limited to small ranges of strength and hardness for each indentation geometry. This relation permits economically important nondestructive testing of bulk metal deliveries with lightweight, even portable equipment, such as hand-held Rockwell hardness testers.

Different techniques are used to quantify material characteristics at smaller scales. Measuring mechanical properties for materials, for instance, of thin films, cannot be done using conventional uniaxial tensile testing. As a result, techniques testing material "hardness" by indenting a material with a very small impression have been developed to attempt to estimate these properties.

Hardness measurements quantify the resistance of a material to plastic deformation. Indentation hardness tests compose the majority of processes used to determine material hardness, and can be divided into three classes: macro, micro and nanoindentation tests. Microindentation tests typically have forces less than 2 N (0.45 lb_f). Hardness, however, cannot be considered to be a fundamental material property.^{[citation needed]} Classical hardness testing usually creates a number that can be used to provide a relative idea of material properties. As such, hardness can only offer a comparative idea of the material's resistance to plastic deformation since different hardness techniques have different scales.

The equation-based definition of hardness is the pressure applied over the contact area between the indenter and the material being tested. As a result, hardness values are typically reported in units of pressure, although this is only a "true" pressure if the indenter and surface interface are perfectly flat.^{[citation needed]}

Instrumented indentation basically indents a sharp tip into the surface of a material to obtain a force-displacement curve. The results provide a lot of information about the mechanical behavior of the material, including hardness, e.g., elastic moduli and plastic deformation. One key factor of the instrumented indentation test is that the tip needs to be controlled by force or displacement that can be measured simultaneously throughout the indentation cycle. Current technology can realize accurate force control in a wide range. Therefore, hardness can be characterized at many different length scales, from hard materials like ceramics to soft materials like polymers.

The earliest work was finished by Bulychev, Alekhin, Shorshorov in the 1970s, who determined that Young's modulus of a material can be determined from the slope of a force vs. displacement indentation curve as:

Where ${\displaystyle E_{s}}$ and ${\displaystyle \nu _{s}}$ are the Young's modulus and Poisson's ratio of the sample, an ${\displaystyle E_{i}}$ and ${\displaystyle \nu _{i}}$ are that of the indenter. Since typically, ${\displaystyle E_{i}>>E_{s}}$, the second term can typically be ignored.