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7.40 For some metal alloy, a true stress of 415 MPa produces a plastic true strain of

0.475. How much will a specimen of this material elongate when a true stress of 325 MPa is applied if the original length is 300 mm ? Assume a value of 0.25 for the strain-hardening exponent n.

7.43 Find the toughness (or energy to cause fracture) for a metal that experiences both

elastic and plastic deformation. Assume Equation 7.5 for elastic deformation, that the modulus of elasticity is 172 GPa , and that elastic deformation terminates at a strain of 0.01. For plastic deformation, assume that the relationship between stress and strain is described by Equation 7.19, in which the values for K and n are 6900 Mpa and 0.30, respectively. Furthermore, plastic deformation occurs between strain values of 0.01 and 0.75, at which point fracture occurs.

7.47 A steel specimen having a rectangular cross section of dimensions 19 mm×3.2

mm (0.75in×0.125in.) has the stress–strain behavior shown in Figure 7.33. If this specimen is subjected to a tensile force of 33,400 N (7,500lbf ), then

(a) Determine the elastic and plastic strain values.

(b) If its original length is 460 mm (18 in.), what will be its final length after the load in part a is applied and then released?

7.50 A three-point bending test was performed on an aluminum oxide specimen

having a circular cross section of radius 3.5 mm; the specimen fractured at a load of 950 N when the distance between the support points was 50 mm . Another test is to be performed on a specimen of this same material, but one that has a square cross section of 12 mm length on each edge. At what load would you expect this specimen to fracture if the support point separation is 40 mm ?

7.51 (a) A three-point transverse bending test is conducted on a cylindrical specimen

of aluminum oxide having a reported flexural strength of 390 MPa . If the speci- men radius is 2.5 mm and the support point separation distance is 30 mm ,

predict whether or not you would expect the specimen to fracture when a load of 620 N is applied. Justify your prediction.

(b) Would you be 100% certain of the prediction in part a? Why or why not?

7.57 When citing the ductility as percent elongation for semicrystalline polymers, it is

not necessary to specify the specimen gauge length, as is the case with metals. Why is this so?

7.66 Using the data represented in Figure 7.31, specify equations relating tensile

strength and Brinell hardness for brass and nodular cast iron, similar to

Equations 7.25a and 7.25b for steels.

8.4 For each of edge, screw, and mixed dislocations, cite the relationship between the

direction of the applied shear stress and the direction of dislocation line motion.

8.5 (a) Define a slip system.

(b) Do all metals have the same slip system? Why or why not?

8.7. One slip system for theBCCcrystal structure is _110__111_. In a manner similar

to Figure 8.6b sketch a _110_-type plane for the BCC structure, representing atom positions with circles. Now, using arrows, indicate two different _111_ slip directions within this plane.

8.15* List four major differences between deformation by twinning and deformation

by slip relative to mechanism, conditions of occurrence, and final result.

8.18 Describe in your own words the three strengthening 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.