HW6+solutions - MechEng 382 Winter 2010 2009 Homework #6...

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MechEng 382 Homework #6 Solutions 1. [ A&J-1 , Ex. 10.1] Show how dislocations can account for the following observations: (a) cold working makes aluminum stronger; Solution Cold working, or work-hardening , involves severe plastic deformations that distort the crystal lattice and accumulate large numbers of dislocations that entangle and prevent further deformation. This resistance results in a stronger material even for a pure metal. (b) an alloy of 20 percent Zn, 80 percent Cu is harder than pure copper; Solution By A&J-1 , Fig. 10.1, this alloy system with the given composition will exist as a single copper-rich solid phase (this can also be veri±ed in consultation with the phase diagram at room temperature). The strengthening mechanism must therefore be solid solution hardening . In particular, the minority Zn will form a random substitutional solid so- lution that distorts the crystal lattice, “roughening” the slip planes as the stress ±elds of dislocation and lattice mismatch, impeding the movement of dislocations, altogether increasing hardness. (c) the hardness of nickel is increased by adding particles of thorium oxide. Solution Here, the impurity oxide co-exists with the Ni in a two-phase solid. The hard particles resist the movement of dislocations, likely by requiring the dislocation to bow around them. This is precipitate/dispersion strengthening . 1 2010
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MechEng 382 Homework #6 Solutions 2. [ A&J-1 , Ex. 10.3] (a) A polycrystalline aluminum alloy contains a dispersion of hard particles of diameter 10 8 m and an average center-to-center spacing of 6 × 10 8 m measured in the slip planes. Estimate their contribution to the tensile strength, σ Y , of the alloy. Solution The relevant mechanism of shear resistance by incoherent precipitates is bowing, since the particles are hard. A free body diagram for a length L of dislocation line during bowing is shown in Fig.
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This note was uploaded on 05/12/2010 for the course MECHENG 382 taught by Professor Thouless during the Winter '08 term at University of Michigan.

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HW6+solutions - MechEng 382 Winter 2010 2009 Homework #6...

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