Brinell hardness equation

Vasic and deMan (1968) defined hardness (H) as the ratio of load to the area of the impression made by the penetrometer. This parameter was explained as the cone will sink into the fat until the stress exerted by the increasing contact surface of the cone is balanced by the hardness of the fat (deMan, 1983). Vasic and deMan (1968) defined fat hardness in a similar way to the Brinell hardness used in metallurgy (Tabor, 1948). The relationship between the applied force load (P), hardness (H), half cone angle (e), radius of the flat tip of the cone (r), penetration impression area (yl jmp) and depth id) for the cone in Figure 7.6 is given by Equation 2 (Vasic and deMan, 1968) ... 

Fourier number based on square root of area critical value of Fourier number radiative parameter for point contact elastoplastic contact parameter gap conductance correlation equation metric coefficients, jacobian height of single and double cones Rockwell C hardness number Brinell hardness... 

Using the data represented in Figure 6.19, specify equations relating tensile strength and Brinell hardness for brass and nodular cast iron, similar to Equations 6.20a and 6.20b for steels. 

The Brinell hardness number (BHN) was first introduced by J. A. Brinell of Sweden in 1900. It is calculated by Equation 3.24 based on the stress per unit surface area of indentation, as illustrated in Figure 3.16. Brinell hardness numbers were usually tabulated in reference charts before the test machine was computerized. The Brinell hardness test is not suitable for very thin specimens due to the depth of indentation impressed onto the part, or very hard materials because of the induced deformation of the tester itself. 

For mild steels, the Brinell hardness number shows a simple empirical relation with the ultimate tensile strength (UTS), as described by Equation 3.25a and b (Budynas and Nisbett, 2008). For certain cast irons, the empirical relationship between ultimate tensile strength and Brinell hardness number is described by Equation 3.25c and d (Krause, 1969). Flowever, the relationships between hardness numbers and tensile strengths are neither universal nor precise. Great caution should be exercised when applying these relationships in reverse engineering analyses. 

Similar to Brinell hardness, Vickers hardness has also been the subject of study to search for a possible relationship between hardness and other mechanical properties. Some semiempirical relationships were reported. Based on a study of a magnesium alloy AZ19 with a nominal composition of Mg-8% Al-0.7% Zn-0.2% Mn-0.002% Fe-0.002% Cu, the flow stress can be approximately calculated by Equation 3.26, where the Vickers hardness number has a nominal unit of kg/mm, and the flow stress is measured in MPa (Caceres, 2002). 

Hardness values are related to flow stress by a constraint factor. It is easy to visualize this by considering a simple compression test because in such a test the whole specimen goes plastic due to the fact that there is no resistance to side flow with the specimen being only surrounded by air. In the indentation test the part of the specimen that flows is surrounded by elastic material and so side flow is restricted. Therefore a greater mean stress is required to cause plastic flow in hardness tests than in simple compression tests. In equation (1.9) C is called the constraint factor, approximating to 3 for Brinell, Vickers, and Knoop hardness. 

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