Page 93 - Manufacturing Engineering and Technology - Kalpakjian, Serope : Schmid, Steven R.

Chapter 2 Mechanical Behavior, Testing, and Manufacturing Properties of Materials

2.6.2 Hardness and Strength
Because hardness is the resistance to permanent indentation, it can be likened to
performing a compression test on a small volume on the surface of a material
(Fig. 2.14c). Studies have shown that (in the same units) the hardness of a cold-
worked metal is about three times its yield stress, Y; for annealed metals, the hard-
ness is about five times Y.
A relationship has been established between the ultimate tensile strength (UTS)
and the Brinell hardness (HB) for steels measured for a load of 3000 kg. In SI units,
the relationship is
UTS = 3.5(I-IB), (2.13)
where UTS is in MPa. In traditional units,
UTS = 500(HB), (2.14)
where UTS is in psi.

2.6.3 Hardness-testing Procedures
For a hardness test to be meaningful and reliable, the zone of deformation under the
indenter (see Fig. 2.14c) must be allowed to develop freely. Consequently, the
location of the indenter (with respect to the edges of the specimen to be tested) and
the thickness of the specimen are important considerations. Generally, the location
should be at least two diameters of the indenter from the edge of the specimen, and
the thickness of the specimen should be at least 10 times the depth of penetration of
the indenter. Successive indentations on the same surface of the workpiece should be
far enough apart so as not to interfere with each other.
Moreover, the indentation should be sufficiently large to give a representative
hardness value for the bulk material. If hardness variations need to be detected in a
small area, or if the hardness of individual constituents in a matrix or an alloy is to
be determined, the indentations should be very small, such as those obtained in
Knoop or Vickers tests using light loads. While surface preparation is not critical for
the Brinell test, it is important for the Rockwell test and even more important for the
other hardness tests, because of the small sizes of the indentations. Surfaces may
have to be polished to allow correct measurement of the impression’s dimensions.
The values obtained from different hardness tests, on different scales, can be
interrelated, and can be converted using Fig. 2.15. Care should be exercised in using
these charts because of the many variables in material characteristics and in the
shape of the indentation.

EXAMPLE 2 2 Calculation of Modulus of Resilience from Hardness
Modulug gf Resilience =
A piece of steel is highly deformed at room tempera- The area under the stress-strain curve is
ture Its hardness is found to be 300 HB. Estimate the 2
area under the stress strain curve up to the yield point
(that is the resilience) for this material if the yield 25
strength is one third the Brinell hardness. prom Table 2_2’ E Z 210 Gpa for Steep

Solutlon Since the steel has been subjected to large Hmce’
strains at room temperature, it may be assumed that its Modulus of Resilience =
stress strain curve has flattened considerably, thus ap-
proaching the shape of a perfectly plastic curve. Since (100)2 >< 9.81 = 0.2336 mm-kg/mm3.
the yield strength is one third the Brinell hardness, 2(21(),()QQ>
300 2
100 kg/mm