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Chapter 7: Problem 37

(a) What is the driving force for recrystallization? (b) What is the driving force for grain growth?

Short Answer

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Answer: (a) The driving force for recrystallization is the stored energy due to the presence of defects (such as dislocations) created during plastic deformation. The material reduces its overall energy by forming new, strain-free grains. (b) The driving force for grain growth is the reduction of total grain boundary energy of the material. As grains grow in size, they eliminate grain boundaries, and reduce the overall grain boundary area, leading to a reduction in the material's total free energy.

Step by step solution

01

(a) Driving Force for Recrystallization

Recrystallization is a process that occurs in materials, where the microstructure of a previously deformed material is replaced by a new, strain-free microstructure, which has a lower energy state. The driving force for recrystallization is the stored energy due to the presence of defects (such as dislocations) created during plastic deformation. By undergoing recrystallization, the material reduces its overall energy, which results in the formation of new, strain-free grains.
02

(b) Driving Force for Grain Growth

Grain growth is a thermally activated process in which the grains of a material grow in size by consuming neighboring grains with high-angle grain boundaries. The driving force for grain growth is the reduction of the total grain boundary energy of the material. As grains grow in size, they eliminate grain boundaries and reduce the overall grain boundary area, which results in a reduction of the material's total free energy. This leads to the material reaching a lower energy state, thus driving the grain growth process.

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Most popular questions from this chapter

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.

Briefly cite the differences between the recovery and recrystallization processes.

As 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.

A single crystal of zinc is oriented for a tensile test such that its slip plane normal makes an angle of \(65^{\circ}\) with the tensile axis. Three possible slip directions make angles of \(30^{\circ}, 48^{\circ}\), and \(78^{\circ}\) with the same tensile axis. (a) Which of these three slip directions is most favored? (b) If plastic deformation begins at a tensile stress of \(2.5 \mathrm{MPa}\) (355 psi), determine the critical resolved shear stress for zinc.

A single crystal of a metal that has the FCC crystal structure is oriented such that a tensile stress is applied parallel to the [100] direction. If the critical resolved shear stress for this material is \(0.5 \mathrm{MPa}\), calculate the magnitude(s) of applied stress(es) necessary to cause slip to occur on the (111) plane in each of the [101], [10\overline{1} ] \text { , and } [ 0 \overline { 1 1 } ] \text { } directions.
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