Page 159 - Mechanical Behavior of Materials

160 Chapter 4 Mechanical Testing: Tension Test and Other Basic Tests

Figure 4.31 Brinell and Rockwell hardness indentations. On the left, in hot-rolled AISI 1020
steel, the larger Brinell indentation has a diameter of 5.4 mm, giving HB = 121, and the
smaller Rockwell B indentation gave HRB = 72. On the right, a higher strength steel has
indentations corresponding to HB = 241 and HRC = 20. (Photo by R. A. Simonds.)

4.7.2 Vickers Hardness Test
The Vickers hardness test is based on the same general principles as the Brinell test. It differs
primarily in that the indenter is a diamond point in the shape of a pyramid with a square base. The
◦
angle between the faces of the pyramid is α = 136 , as shown in Fig. 4.32. This shape results in the
depth of penetration, h, being one-seventh of the indentation size, d, measured on the diagonal.
The Vickers hardness number HV is obtained by dividing the applied force P by the surface area of
the pyramidal depression. This yields

2P α
HV = 2 sin (4.30)
d 2
where d is in millimeters and P in kilograms.
Note that the standard pyramidal shape causes the indentations to be geometrically similar,
regardless of their size. For reasons derived from plasticity theory and which are beyond the scope
of the present discussion, this geometric similarity is expected to result in a Vickers hardness value
that is independent of the magnitude of the force used. Hence, a wide range of standard forces
usually between 1 and 120 kg are used, so that essentially all solid materials can be included in a
single wide-ranging hardness scale.
Approximate Vickers hardness numbers are given for various classes of materials in Fig. 4.29.
Also, values for some ceramics are given in Table 4.7. Within the more limited range where the
Brinell test can be used, there is approximate agreement with the Vickers scale. This approximate
agreement is shown, by average curves for steels of various strengths, in Fig. 4.33.