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is then withdrawn from the machine and the operator measures the diameter of the indentation by means of a millimeter scale etched on the eyepiece of a special Brinell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 = L ( D/2)[D (D2 d 2)1/2] (32.2)
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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.
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32.8.3 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 HM = 4L d 2 (32.3)
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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
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L = Ad p where L = load on spherical indenter d = diameter of indentation p = Meyer strain-hardening exponent
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(32.4)
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. (32.4) is related to the strain-strengthening exponent m in the tensile stress-strain equation = 0 m, which is to be presented later. The relation is p 2=m (32.5)
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.
32.8.4 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 Hp = 2L sin ( /2) 1.8544L = d2 d2 (32.6)
where L = applied load, kg d = diagonal of the indentation, mm = 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 num-
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