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Strengthening mechanisms and dislocations

The yield stress of BCC metals such as iron rises sharply as the temperature is lowered, whereas in FCC metals such as copper and aluminum it changes little with temperature. Which is the main cause of this difference?

  1. AIn FCC metals the stacking-fault energy falls at low temperature and dislocations dissociate and move more easily, so the yield stress actually falls at low temperature
  2. BIn BCC metals interstitial carbon and nitrogen gather more readily at dislocations at low temperature, so pinning by Cottrell atmospheres grows stronger as the temperature falls
  3. CThe cores of screw dislocations in BCC metals spread over several planes and move with difficulty, overcoming the lattice resistance with the help of thermal fluctuations, so more stress is needed at lower temperature
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Answer: C. The cores of screw dislocations in BCC metals spread over several planes and move with difficulty, overcoming the lattice resistance with the help of thermal fluctuations, so more stress is needed at lower temperature

The cores of screw dislocations in BCC metals do not spread flat on a single plane but take a three-dimensional form extending over several {110} planes, so the Peierls stress, the resistance of the lattice to dislocation motion, is large. Dislocations cross this barrier a little at a time with the help of thermal fluctuations (formation of kink pairs), so as the temperature falls this help diminishes and the yield stress rises steeply. This is one reason for the ductile-to-brittle transition of BCC steels. Dislocations in FCC metals are dissociated flat on the close-packed planes, the Peierls stress is small and the yield stress depends little on temperature. The option in which the yield stress falls at low temperature contradicts the facts, and high-purity BCC metals free of carbon and nitrogen show the same temperature dependence, so the option attributing it mainly to Cottrell atmospheres is also wrong.

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More Strengthening mechanisms and dislocations questions

  1. In a substitutional solid solution, assume that the increase in yield stress Δσ is proportional to the square root of the solute concentration c (the Fleischer model). If Δσ = 30 MPa at 1 at% solute, which is closest to Δσ at 4 at% solute? Ignore interactions between solute atoms and precipitation.
  2. When annealed low-carbon steel is pulled in tension, the stress drops after an upper yield point and a yield-point phenomenon appears in which Lüders bands travel along the specimen. Which statement about this phenomenon and its remedy is correct?
  3. The flow stress of a work-hardened metal is estimated with the Taylor equation σ = MαGb√ρ (ρ is the dislocation density). For cold-worked copper with M = 3.06, α = 0.3, G = 48 GPa, b = 0.256 nm and ρ = 1.0×10¹⁴ m⁻², which is closest to σ?
  4. When a metal is plastically deformed in tension, unloaded and then compressed in the reverse direction, the yield stress in compression is lower than the flow stress it would have had if tension had continued. Which is the correct explanation of this phenomenon (the Bauschinger effect)?
  5. As precipitates grow during aging, the strength rises to a maximum and then falls (overaging). Which is the correct explanation in terms of the interaction between precipitates and dislocations? Take the volume fraction of precipitates as constant.