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Materials Science and Engineering: An Introduction

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Unformatted text preview: REVISED PAGES 204 - Chapter? I Dislocations and Strengthening Mechanisms applied tensile stress of 13.9 MPa (2020 psi), compute the critical resolved shear stress. 7.15 A single crystal of a metal that has the FCC crystal structure is oriented such that a ten- sile stress is applied parallel to the [100] di- rection. If the critical resolved shear stress for this material is 0.5 MPa, calculate the magni- tude(s) of applied stress(es) necessary to cause slip to occur on the (111) plane in each of the [110], [101], and {011] directions. 7.16 (a) A single crystal of a metal that has the BCC crystal structure is oriented such that a tensile stress is applied in the [100] direction. If the magnitude of this stress is 4.0 MPa, com- pute the resolved shear stress in the [111] di- rection on each of the (110), (011), and (101) planes. (1)) 0n the basis of these resolved shear stress values, which slip system(s) is (are) most fa- vorably oriented? 7.17 Consider a single crystal of some hypothet— ical metal that has the BCC crystal structure and is oriented such that a tensile stress is applied along a [121] directionLIf slip oc- curs on a (101) plane and in a [111] direcn tion, compute the stress at which the crystal yields if its critical resolved shear stress is 2.4 MPa. 7.18 The critical resolved shear stress for copper is 0.48 MPa (70 psi). Determine the maximum possible yield strength for a single crystal of Cu pulled in tension. Deformation by Twinning 7.19 List four major differences between defor- mation by twinning and deformation by slip relative to mechanism, conditions of occur- rence, and final result. Strengthening by Grain Size Reduction 7.20 Briefly explain Why small-angle grain bound- aries are not as effective in interfering with the slip process as are high-angle grain boundaries 7.21 Briefly explain why HCP metals are typically more brittle than FCC and BCC metals. 7.22 Describe in your own words the three strength— ening mechanisms discussed in this chapter (i.e., grain size reduction, solid-solution strengthening, and strain hardening). Be sure to explain how dislocations are involved in each of the strengthening techniques 7.23 (a) From the plot of yield strength versus (grain diameter)'”2 for a 70 Cu—30 Zn car- tridge brass, Figure 7.15, determine values for the constants (To and ky in Equation 7.7. (it) Now predict the yield strength of this alloy when the average grain diameter is 2.0 X 10“3 mm. 7.24 The lower yield point for an iron that has an average grain diameter of 1 X 10’2 mm is 230 MPa (33,000 psi). At a grain diameter of 6 X 10'3 nun, the yield point increases to 275 MPa (40,000 psi). At what grain diame- ter will the lower yield point be 310 MPa (45,000 psi)? 7.25 If it is assumed that the plot in Figure 7.15 is for noncold—worked brass determine the grain size of the alloy in Figure 7.19; assume its com- position is the same as the alloy in Figure 7.15. Solid-SOMtiOH Strengthening 7.26 In the manner of Figures 7.17.!) and 7.18b, in« dicate the location in the vicinity of an edge dislocation at which an interstitial impurity atom would be expected to be situated. Now briefly explain in terms of lattice strains why it would be situated at this position. Strain Hardening 7.27 (a) Show, for a tensile test, that E %CW=( )XlOO 6+1 if there is no change in specimen volume dur- ing the deformation process (i.e.,Anlo = Adid). (b) Using the result of part (a), compute the percent coid work experienced by naval brass (for which the stress—strain behavior is shown in Figure 6.12) when a stress of 415 MPa (60,000 psi) is applied. 7.28 Two previously undeformed cylindrical spec- imens of an alloy are to be strain hardened by reducing their cross-sectional areas (while maintaining their circular cross sections). For one specimen, the initial and deformed radii are 15 mm and 12 mm, respectively. The sec- ond specimen, with an initial radius of 11 mm, EQA ...
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