Hardness and Tensile Strength Relationship

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). 

The relationship between hardness and other mechanical properties will be further discussed in Chapter 6 from the perspective of statistical regression. 

Standard test methods for determining average grain size. ASTM E112-96(2004)e2. West Conshohocken, PA ASTM Intemational. 

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