2.Fundamental Mechanical Properties of Materials 21 In o Plastic region Plastic region slope n<I Elastic region (b) Elastic region slope n=1 In er FIGURE 2.9.(a)True stress versus true strain diagram (compare to (a) Figure 2.4).(b)In ot versus In e diagram. In many cases,and before necking begins,one can approximate the true stress-true strain curve by the following empirical equation: :=K(e)", (2.7) where n is the strain hardening exponent (having values of less than unity)and K is another materials constant (called the strength coefficient)which usually amounts to several hundred MPa.Taking the (natural)logarithm of Eq.(2.7)yields: In o:=n In e+In K, (2.8) which reveals that the strain hardening exponent(or strain hard- ening rate),n,is the slope in the plastic portion of an In o versus In e diagram,see Figure 2.9(b). The tensile test and the resulting stress-strain diagrams have been shown above to provide a comprehensive insight into many of the mechanical properties of materials.For specialized appli- cations,however,a handful of further tests are commonly used. Some of them will be reviewed briefly below. The hardness test is nondestructive and fast.A small steel sphere (commonly 10 mm in diameter)is momentarily pressed into the surface of a test piece.The diameter of the indentation is then measured under the microscope,from which the Brinell hard- ness number(BHN)is calculated by taking the applied force and the size of the steel sphere into consideration.The BHN is directly proportional to the tensile strength.(The Rockwell hardness tester uses instead a diamond cone and measures the depth of the in- dentation under a known load whereas the Vickers and Knoop mi- crohardness techniques utilize diamond pyramids as indenters.) Materials,even when stressed below the yield strength,still may eventually break if a large number of tension and compres-Elastic region Plastic region slope n=1 ln t ln t slope n<1 In many cases, and before necking begins, one can approximate the true stress–true strain curve by the following empirical equation: t
K(t)n, (2.7) where n is the strain hardening exponent (having values of less than unity) and K is another materials constant (called the strength coefficient) which usually amounts to several hundred MPa. Taking the (natural) logarithm of Eq. (2.7) yields: ln t
n ln t ln K, (2.8) which reveals that the strain hardening exponent (or strain hard￾ening rate), n, is the slope in the plastic portion of an ln t versus ln t diagram, see Figure 2.9(b). The tensile test and the resulting stress–strain diagrams have been shown above to provide a comprehensive insight into many of the mechanical properties of materials. For specialized appli￾cations, however, a handful of further tests are commonly used. Some of them will be reviewed briefly below. The hardness test is nondestructive and fast. A small steel sphere (commonly 10 mm in diameter) is momentarily pressed into the surface of a test piece. The diameter of the indentation is then measured under the microscope, from which the Brinell hard￾ness number (BHN) is calculated by taking the applied force and the size of the steel sphere into consideration. The BHN is directly proportional to the tensile strength. (The Rockwell hardness tester uses instead a diamond cone and measures the depth of the in￾dentation under a known load whereas the Vickers and Knoop mi￾crohardness techniques utilize diamond pyramids as indenters.) Materials, even when stressed below the yield strength, still may eventually break if a large number of tension and compres- 2 • Fundamental Mechanical Properties of Materials 21 FIGURE 2.9. (a) True stress versus true strain diagram (compare to Figure 2.4). (b) ln t versus ln t diagram. y t t Plastic region Elastic region T (a) (b)