Material Hardness and Its Relation With Tensile Strength

When you hear of material hardness, it may be difficult to differentiate between that and other similar material properties such as strength, stiffness, and toughness. I cover strength and stiffness in Strength, Stiffness, and Stability of Materials, but let’s talk about hardness and how it may potentially affect your choice of materials.

Hardness is defined as a measure of a solid material’s resistance to permanent shape-change or deformation when a force is applied. A material’s hardness is actually dependent on the various other factors such as its strength, elasticity, and toughness. There are three different classifications of hardness: scratch hardness, indentation hardness, and rebound hardness.

rough diamond still in matrix

Let’s walk through these three classifications and see if we can’t gain a better understanding.

Scratch Hardness

Scratch hardness is a measure of the resistance of a sample material to permanent deformation or fracture due to a sharp, hard object. A common way of performing this measurement is by using what’s called a sclerometer, which is a diamond tipped tool to scratch a sample object under a fixed load and under fixed conditions. The scratch hardness of the material can be determined by measuring the width of the resulting microscopic scratch.

Indentation Hardness

The most used and perhaps the most known of the three, indentation hardness is the measure of a material to permanent deformation by way of a sharp object under a constant or varying compression load. Although there are many types of indentation tests under different names, with varying indenter profiles, they generally all employ the same basic principles:

1. Lower an indenter of known characteristics (material-type, size, shape, hardness, etc), onto a test sample of unknown hardness with a specified load for a specified period of time.
2. Release all or a portion of the load and measure either the depth or surface area of the resultant indentation.

Rockwell hardness test

Rockwell scale diagram showing forces

Indentation hardness tests are subdivided into macroindentation, microindentation, or nanoindentation, depending on the applied load; >1000 gf, between 1 and 1000 gf, and <1 gf respectively. Indentation hardness tests have gained popularity due to the small scale and ease with which tests can be carried out. Test samples and apparatus can be small, with virtually no resulting visual or mechanical damage. Calculations must be corrected to compensate for strain-hardening and/or nonuniformity of sample material. However, both these effects can be minimized if not nullified by smaller (micro or nanoindentation) and/or multiple indentations.

Linear Correlation between Hardness and Tensile strength

Another interesting point about indentation hardness is its linear correlation with the tensile strength of various monolithic metals. Simply put, an increase in hardness indicates an increase in tensile strength. Care should be taken however, as resulting values can be highly subject to the effect of any constituent alloying metals.

Linear Relationship for AA7050

The hardness/strength linear correlation for high strength AA7050 aluminum alloy

There have been numerous studies and tests conducted on this particular relationship between hardness and tensile strength, but the general consensus is that all “proof” of a linear relationship is achieved through empirical testing in both hardness and tension, and cannot be extrapolated or otherwise calculated concerning untested sample materials.

For a more comprehensive study on this correlation:

General relationship between strength and hardness

Rebound Hardness

Also known as dynamic hardness, rebound hardness is a measure of the height of the bounce due to a diamond-tipped hammer being dropped from a fixed height on a sample material. The material’s elasticity plays a major role in this form of hardness.

The Confusion Between Hardness and Stiffness, and the Role of Shear Modulus

Hardness is often mistaken for stiffness due to both words having more or less similar meanings by common definition. However, there are some fundamental differences in the technical sense. Stiffness can be defined as an elastic material’s ability to resist deformation along a given degree of freedom, whereas hardness is based on the smaller-scale microdurability of the material.

Rather than properties such as bulk modulus, Young’s modulus, and stiffness, hardness is based on a material’s shear modulus. When a diamond-tipped tool is lowered onto a sample material during a typical hardness test, it attempts to cut into the material, essentially causing a small, local failure in shear. The shear modulus of a metal is usually higher when alloyed, due to an additional foreign source of shear resistance.

The five hardest naturally occurring chemical elements in the world are diamond, boron, chromium, tungsten, and vanadium in this order. There are however, man-made nanomaterials that are considerably harder than diamond. One thing to remember is that even among diamonds, there is considerable variation in hardness depending on the level of impurities contained within them.

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