Hardness

Hardness is used more frequently than any other of the mechanical properties by
the design engineer to specify the final condition of a structural part. This is due in
part to the fact that hardness tests are the least expensive in time and money to conduct.
The test can be performed on a finished part without the need to machine a
special test specimen. In other words, a hardness test may be a nondestructive test in
that it can be performed on the actual part without affecting its service function.
Hardness is frequently defined as a measure of the ability of a material to resist
plastic deformation or penetration by an indenter having a spherical or conical end.
At the present time, hardness is more a technological property of a material than it
is a scientific or engineering property. In a sense, hardness tests are practical shop
tests rather than basic scientific tests. All the hardness scales in use today give relative
values rather than absolute ones. Even though some hardness scales, such as the
Brinell, have units of stress (kg/mm2) associated with them, they are not absolute
scales because a given piece of material (such as a 2-in cube of brass) will have significantly
different Brinell hardness numbers depending on whether a 500-kg or a
3000-kg load is applied to the indenter.
Rockwell Hardness
The Rockwell hardnesses are hardness numbers obtained by an indentation type of
test based on the depth of the indentation due to an increment of load. The Rockwell
scales are by far the most frequently used hardness scales in industry even
though they are completely relative. The reasons for their large acceptance are the
simplicity of the testing apparatus, the short time necessary to obtain a reading, and
the ease with which reproducible readings can be obtained, the last of these being
due in part to the fact that the testing machine has a "direct-reading" dial; that is, a
needle points directly to the actual hardness value without the need for referring to
a conversion table or chart, as is true with the Brinell, Vickers, or Knoop hardnesses.
Indenter 1 is a diamond cone having an included angle of 120° and a spherical
end radius of 0.008 in. Indenters 2 and 3 are Me-in-diameter and ^-in-diameter balls,
respectively. In addition to the preceding scales, there are several others for testing
very soft bearing materials, such as babbit, that use ^-in-diameter and M-in-diameter
balls. Also, there are several "superficial" scales that use a special diamond cone with
loads less than 50 kg to test the hardness of surface-hardened layers.
The particular materials that each scale is used on are as follows: the A scale on
the extremely hard materials, such as carbides or thin case-hardened layers on steel;
the B scale on soft steels, copper and aluminum alloys, and soft-case irons; the C
scale on medium and hard steels, hard-case irons, and all hard nonferrous alloys; the
E and F scales on soft copper and aluminum alloys. The remaining scales are used on
even softer alloys.
Several precautions must be observed in the proper use of the Rockwell scales.
The ball indenter should not be used on any material having a hardness greater than
50 RC, otherwise the steel ball will be plastically deformed or flattened and thus give
erroneous readings. Readings taken on the sides of cylinders or spheres should be
corrected for the curvature of the surface. Readings on the C scale of less than 20
should not be recorded or specified because they are unreliable and subject to much
variation.
The hardness numbers for all the Rockwell scales are an inverse measure of the
depth of the indentation. Each division on the dial gauge of the Rockwell machine
corresponds to an 80 x 106 in depth of penetration. The penetration with the C scale
varies between 0.0005 in for hard steel and 0.0015 in for very soft steel when only the
minor load is applied. The total depth of penetration with both the major and minor
loads applied varies from 0.003 in for the hardest steel to 0.008 in for soft steel (20
RC). Since these indentations are relatively shallow, the Rockwell C hardness test is
considered a nondestructive test and it can be used on fairly thin parts.
Although negative hardness readings can be obtained on the Rockwell scales
(akin to negative Fahrenheit temperature readings), they are usually not recorded as
such, but rather a different scale is used that gives readings greater than zero. The
only exception to this is when one wants to show a continuous trend in the change in
hardness of a material due to some treatment. A good example of this is the case of
the effect of cold work on the hardness of a fully annealed brass. Here the annealed
hardness may be -20 RB and increase to 95 R8 with severe cold work.

Brinell Hardness
The Brinell hardness H8 is the hardness number obtained by dividing the load that
is applied to a spherical indenter by the surface area of the spherical indentation
produced; it has units of kilograms per square millimeter. Most readings are taken
with a 10-mm ball of either hardened steel or tungsten carbide. The loads that are
applied vary from 500 kg for soft materials to 3000 kg for hard materials. The steel
ball should not be used on materials having a hardness greater than about 525 H8
(52 RC) because of the possibility of putting a flat spot on the ball and making it inaccurate
for further use.
The Brinell hardness machine is as simple as, though more massive than, the
Rockwell hardness machine, but the standard model is not direct-reading and takes
a longer time to obtain a reading than the Rockwell machine. In addition, the indentation
is much larger than that produced by the Rockwell machine, and the machine
cannot be used on hard steel. The method of operation, however, is simple. The prescribed
load is applied to the 10-mm-diameter ball for approximately 10 s. The part
is then withdrawn from the machine and the operator measures the diameter of the
indentation by means of a millimeter scale etched on the eyepiece of a special
Brinell microscope. The Brinell hardness number is then obtained from the equation
HB = (nD/2)[D-(D2-d2)l/2] (?'2)
where L = load, kg
D = diameter of indenter, mm
d = diameter of indentation, mm
The denominator in this equation is the spherical area of the indentation.
The Brinell hardness test has proved to be very successful, partly due to the fact
that for some materials it can be directly correlated to the tensile strength. For example,
the tensile strengths of all the steels, if stress-relieved, are very close to being 0.5
times the Brinell hardness number when expressed in kilopounds per square inch
(kpsi).This is true for both annealed and heat-treated steel. Even though the Brinell
hardness test is a technological one, it can be used with considerable success in engineering
research on the mechanical properties of materials and is a much better test
for this purpose than the Rockwell test.
The Brinell hardness number of a given material increases as the applied load is
increased, the increase being somewhat proportional to the strain-hardening rate of
the material. This is due to the fact that the material beneath the indentation is plastically
deformed, and the greater the penetration, the greater is the amount of cold
work, with a resulting high hardness. For example, the cobalt base alloy HS-25 has a
hardness of 150 HB with a 500-kg load and a hardness of 201 HB with an applied load
of 3000 kg.

Meyer Hardness
The Meyer hardness HM is the hardness number obtained by dividing the load
applied to a spherical indenter by the projected area of the indentation. The Meyer
hardness test itself is identical to the Brinell test and is usually performed on a
Brinell hardness-testing machine. The difference between these two hardness scales
is simply the area that is divided into the applied load—the projected area being used
for the Meyer hardness and the spherical surface area for the Brinell hardness. Both
are based on the diameter of the indentation. The units of the Meyer hardness are
also kilograms per square millimeter, and hardness is calculated from the equation
»»=%
Because the Meyer hardness is determined from the projected area rather than
the contact area, it is a more valid concept of stress and therefore is considered a
more basic or scientific hardness scale. Although this is true, it has been used very little
since it was first proposed in 1908, and then only in research studies. Its lack of
acceptance is probably due to the fact that it does not directly relate to the tensile
strength the way the Brinell hardness does.
Meyer is much better known for the original strain-hardening equation that
bears his name than he is for the hardness scale that bears his name. The strainhardening
equation for a given diameter of ball is
L=Adp (7.4)
where L = load on spherical indenter
d = diameter of indentation
p = Meyer strain-hardening exponent
The values of the strain-hardening exponent for a variety of materials are available
in many handbooks. They vary from a minimum value of 2.0 for low-work-hardening
materials, such as the PH stainless steels and all cold-rolled metals, to a maximum of
about 2.6 for dead soft brass. The value of p is about 2.25 for both annealed pure aluminum
and annealed 1020 steel.
Experimental data for some metals show that the exponent p in Eq. (7.4) is
related to the strain-strengthening exponent m in the tensile stress-strain equation
a = O0em, which is to be presented later. The relation is
p-2 = m (7.5)
In the case of 70-30 brass, which had an experimentally determined value of p = 2.53,
a separately run tensile test gave a value of m = 0.53. However, such good agreement
does not always occur, partly because of the difficulty of accurately measuring
the diameter d. Nevertheless, this approximate relationship between the strainhardening
and the strain-strengthening exponents can be very useful in the practical
evaluation of the mechanical properties of a material.

Vickers or Diamond-Pyramid Hardness
The diamond-pyramid hardness Hp, or the Vickers hardness Hv, as it is frequently
called, is the hardness number obtained by dividing the load applied to a squarebased
pyramid indenter by the surface area of the indentation. It is similar to the
Brinell hardness test except for the indenter used. The indenter is made of industrial
diamond, and the area of the two pairs of opposite faces is accurately ground to an
included angle of 136°. The load applied varies from as low as 100 g for microhardness
readings to as high as 120 kg for the standard macrohardness readings. The
indentation at the surface of the workpiece is square-shaped. The diamond pyramid
hardness number is determined by measuring the length of the two diagonals of the
indentation and using the average value in the equation
rr 2L sin (a/2) 1.8544L ,_ ^
Hp = d* =~^~ (7'6)
where L = applied load, kg
d = diagonal of the indentation, mm
a = face angle of the pyramid, 136°
The main advantage of a cone or pyramid indenter is that it produces indentations
that are geometrically similar regardless of depth. In order to be geometrically
similar, the angle subtended by the indentation must be constant regardless of the
depth of the indentation. This is not true of a ball indenter. It is believed that if geometrically
similar deformations are produced, the material being tested is stressed to
the same amount regardless of the depth of the penetration. On this basis, it would
be expected that conical or pyramidal indenters would give the same hardness number
regardless of the load applied. Experimental data show that the pyramid hardness
number is independent of the load if loads greater than 3 kg are applied. However,
for loads less than 3 kg, the hardness is affected by the load, depending on the
strain-hardening exponent of the material being tested.

Knoop Hardness
The Knoop hardness HK is the hardness number obtained by dividing the load applied
to a special rhombic-based pyramid indenter by the projected area of the indentation.
The indenter is made of industrial diamond, and the four pyramid faces are ground so
that one of the angles between the intersections of the four faces is 172.5° and the
other angle is 130°. A pyramid of this shape makes an indentation that has the projected
shape of a parallelogram having a long diagonal that is 7 times as large as the
short diagonal and 30 times as large as the maximum depth of the indentation.
The greatest application of Knoop hardness is in the microhardness area. As
such, the indenter is mounted on an axis parallel to the barrel of a microscope having
magnifications of 10Ox to 50Ox. A metallurgically polished flat specimen is used.
The place at which the hardness is to be determined is located and positioned under
the hairlines of the microscope eyepiece. The specimen is then positioned under the
indenter and the load is applied for 10 to 20 s.The specimen is then located under the
microscope again and the length of the long diagonal is measured. The Knoop hardness
number is then determined by means of the equation
HK = 0.070 28d* (7'7)
where L = applied load, kg
d = length of long diagonal, mm
The indenter constant 0.070 28 corresponds to the standard angles mentioned
above.

Scleroscope Hardness
The scleroscope hardness is the hardness number obtained from the height to which a
special indenter bounces. The indenter has a rounded end and falls freely a distance of
10 in in a glass tube. The rebound height is measured by visually observing the maximum
height the indenter reaches. The measuring scale is divided into 140 equal divisions
and numbered beginning with zero. The scale was selected so that the rebound
height from a fully hardened high-carbon steel gives a maximum reading of 100.
All the previously described hardness scales are called static hardnesses because
the load is slowly applied and maintained for several seconds. The scleroscope hardness,
however, is a dynamic hardness. As such, it is greatly influenced by the elastic
modulus of the material being tested.