Chapter 7: Problem 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.
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Chapter 7: Problem 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.
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Two previously undeformed cylindrical specimens 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 and \(12 \mathrm{~mm}\), respectively. The second specimen, with an initial radius of \(11 \mathrm{~mm}\), must have the same deformed hardness as the first specimen; compute the second specimen's radius after deformation.
To provide some perspective on the dimensions of atomic defects, consider a metal specimen with a dislocation density of \(10^{5} \mathrm{~mm}^{-2}\). Suppose that all the dislocations in \(1000 \mathrm{~mm}^{3}\left(1 \mathrm{~cm}^{3}\right)\) were somehow removed and linked end to end. How far (in miles) would this chain extend? Now suppose that the density is increased to \(10^{9} \mathrm{~mm}^{-2}\) by cold working. What would be the chain length of dislocations in \(1000 \mathrm{~mm}^{3}\) of material?
A cylindrical specimen of a metal alloy \(10 \mathrm{~mm}\) \((0.4\) in.) in diameter is stressed elastically in tension. A force of \(15,000 \mathrm{~N}\left(3370 \mathrm{lb}_{\mathrm{f}}\right.\) ) produces a reduction in specimen diameter of \(7 \times 10^{-3} \mathrm{~mm}\) \(\left(2.8 \times 10^{-4}\right.\) in.). Compute Poisson's ratio for this material if its elastic modulus is \(100 \mathrm{GPa}(14.5 \times\) \(\left.10^{6} \mathrm{psi}\right)\)
A cylindrical rod of steel \(\left(E=207 \mathrm{GPa}, 30 \times 10^{\circ}\right.\) psi) having a yield strength of \(310 \mathrm{MPa}(45,000\) psi) is to be subjected to a load of \(11,100 \mathrm{~N}\) (2500 \(\left.\mathrm{Ib}_{i}\right)\). If the length of the rod is \(500 \mathrm{~mm}(20.0 \mathrm{in}\).), what must be the diameter to allow an elongation of \(0.38 \mathrm{~mm}(0.015\) in.)?
A specimen of copper having a rectangular cross section \(15.2 \mathrm{~mm} \times 19.1 \mathrm{~mm}(0.60 \mathrm{in} . \times 0.75 \mathrm{in} .)\) is pulled in tension with \(44,500 \mathrm{~N}\left(10,000 \mathrm{lb}_{\mathrm{f}}\right)\) force, producing only elastic deformation. Calculate the resulting strain.
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