Chapter 7: Problem 20
List four major differences between deformation by twinning and deformation by slip relative to mechanism, conditions of occurrence, and final result.
Chapter 7: Problem 20
List four major differences between deformation by twinning and deformation by slip relative to mechanism, conditions of occurrence, and final result.
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Get started for freeAs noted in Section \(3.15\), for single crystals of some substances, the physical properties are anisotropic that is, they depend on crystallographic direction. One such property is the modulus of elasticity. For cubic single crystals, the modulus of elasticity in a general \([u v w]\) direction, \(E_{\text {uww }}\) is described by the relationship $$ \begin{aligned} \frac{1}{E_{u v w}}=& \frac{1}{E_{(100)}}-3\left(\frac{1}{E_{(100)}}-\frac{1}{E_{\\{111)}}\right) \\\ &\left(\alpha^{2} \beta^{2}+\beta^{2} \gamma^{2}+\gamma^{2} \alpha^{2}\right) \end{aligned} $$ where \(E_{\\{100)}\) and \(E_{\langle 111\rangle}\) are the moduli of elasticity in the \([100]\) and \([111]\) directions, respectively; \(\alpha, \beta\), and \(\gamma\) are the cosines of the angles between \([u v w]\) and the respective [100], [010], and [001] directions. Verify that the \(E_{\\{110\rangle}\) values for aluminum, copper, and iron in Table \(3.4\) are correct.
6.24 A cylindrical rod \(120 \mathrm{~mm}\) long and having a (- diameter of \(15.0 \mathrm{~mm}\) is to be deformed using a tensile load of \(35,000 \mathrm{~N}\). It must not experience either plastic deformation or a diameter reduction of more than \(1.2 \times 10^{-2} \mathrm{~mm}\). Of the following materials listed, which are possible candidates? Justify your choice(s). \begin{tabular}{lccc} \hline & Modulus of Material & \begin{tabular}{c} \mathrm{ Yield } \(\\\ {\text { Elasticity }} \\ {\text { (GPa) }}\) & Strength (MPa) & Poisson's Ratio \\ \hline Aluminum alloy & 70 & 250 & \(0.33\) \\ \hline Titanium alloy & 105 & 850 & \(0.36\) \\ \hline Steel alloy & 205 & 550 & \(0.27\) \\ \hline Magnesium alloy & 45 & 170 & \(0.35\) \\ \hline \end{tabular} \end{tabular}
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.
Consider a metal single crystal oriented such that the normal to the slip plane and the slip direction are at angles of \(60^{\circ}\) and \(35^{\circ}\), respectively, with the tensile axis. If the critical resolved shear stress is \(6.2 \mathrm{MPa}\) (900 psi), will an applied stress of 12 MPa (1750 psi) cause the single crystal to yield? If not, what stress will be necessary?
Consider a cylindrical specimen of some hypothetical metal alloy that has a diameter of \(10.0\) \(\mathrm{mm}(0.39 \mathrm{in} .) .\) A tensile force of \(1500 \mathrm{~N}\left(340 \mathrm{lb}_{\mathrm{f}}\right)\) produces an elastic reduction in diameter of \(6.7 \times 10^{-4} \mathrm{~mm}\left(2.64 \times 10^{-5}\right.\) in.). Compute the elastic modulus of this alloy, given that Poisson's ratio is \(0.35\).
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