296 8-10 A 0.505-in.-diameter metal bar with a 2-in. gage length o is subjected to a tensile test. The following measurements are made in the plastic region: 8-13 Chapter 8 Strain Hardening and Annealing Figure 8-23 shows a plot of the natural log- arithm of the true stress versus the natural logarithm of the true strain for a Cu-30% Zn sample tested in tension. Only the plastic portion of the stress strain curve is shown. Determine the strength coefficient K and the work-hardening exponent n. Change in Force Gage length Diameter (lb) (in.) (Al) (in.) 21 27,500 0.2103 0.4800 27,000 0.4428 0.4566 20 25,700 0.6997 0.4343 8-11 Determine the strain-hardening exponent for the metal. Is the metal most likely to be FCC, BCC, or HCP? Explain. A 1.33-cm-diameter metal bar with a 3-cm gage length (10) is subjected to a ten- sile test. The following measurements are made in the plastic region: In [True stress (Pa)] 18 16 -2.5 -2.0 -1.5 -1.0 -0.5 -0.0 In (True strain) Figure 8-23 The natural logarithm of the true stress versus the natural logarithm of the true strain for a Cu-30% Zn sample tested in tension. Only the plastic portion of the stress strain curve is shown. Force (N) Change in Gage length (cm) 16,240 0.6642 19,066 1.4754 Diameter (cm) 1.2028 1.0884 8-14 19,273 2.4663 0.9848 Determine the strain-hardening coefficient for the metal. Is the metal most likely to be FCC, BCC, or HCP? Explain. 8-12 A true stress-true strain curve is shown in Figure 8-22. Determine the strain- hardening exponent for the metal. 8.15 A Cu-30% Zn alloy tensile bar has a strain hardening coefficient of 0.50. The bar, which has an initial diameter of 1 cm and an initial gage length of 3 cm, fails at an engineering stress of 120 MPa. At the moment of fracture, the gage length is 3.5 cm and the diameter is 0.926 cm. No necking occurred. Calculate the true stress when the true strain is 0.05 cm/cm. What would a strain hardening exponent of