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Strengthening mechanisms and dislocations

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.

  1. ASmall precipitates are bypassed by dislocations and larger ones come to be sheared, and the stress needed to shear them increases as the spacing between precipitates widens
  2. BSmall precipitates are sheared by dislocations with a resistance that grows with their size, but larger ones are passed by dislocations bowing out between them, at a stress that falls as the spacing widens
  3. CPrecipitates of every size are sheared, and as they grow their coherency with the matrix increases so the shearing resistance keeps rising, while the maximum strength is set by the loss of solid-solution strengthening
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Answer: B. Small precipitates are sheared by dislocations with a resistance that grows with their size, but larger ones are passed by dislocations bowing out between them, at a stress that falls as the spacing widens

The small, coherent precipitates of early aging are sheared and passed through by dislocations. The resistance to shearing comes from the work of creating coherency strain, new interface and, for ordered phases, an antiphase boundary, and at a constant volume fraction it increases as the precipitates grow. Once precipitates become large, it becomes easier for dislocations to bow out between them and pass, leaving loops (the Orowan mechanism), and that stress is inversely proportional to the precipitate spacing, so it falls as the particles coarsen. The strength peaks at the size where the two mechanisms change over, which corresponds to peak aging. The option with the order of bypassing and shearing reversed is wrong. Precipitates tend to lose coherency with the matrix as they grow, so the option in which coherency increases is also wrong.

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More Strengthening mechanisms and dislocations questions

  1. In an aluminum alloy, the increase in shear stress due to the Orowan mechanism, in which dislocations bow out and pass between precipitates, is estimated as Δτ ≈ Gb/L (L is the precipitate spacing). With G = 26 GPa, b = 0.286 nm and L = 100 nm, and taking the increase in the yield stress of the polycrystal as Δσ = MΔτ (Taylor factor M = 3.06), which is closest to Δσ?
  2. Which statement about the characteristics of dislocations shearing through precipitates with an ordered structure, such as the γ' phase (an L1₂ ordered phase) in Ni-based superalloys, is correct?
  3. Which statement about dispersion strengthening with oxide particles, as in copper containing fine Al₂O₃ particles or ODS steels with Y₂O₃ particles dispersed in iron, is correct?
  4. The yield stress of an alloy is estimated from contributions of 50 MPa friction stress, 60 MPa solid-solution strengthening, 200 MPa precipitation strengthening and 100 MPa dislocation strengthening. If the friction stress and solid-solution strengthening are simply added, while the contributions of precipitates and dislocations, which are obstacles of similar strength, are combined as the square root of the sum of squares (σ = σ₀ + σss + √(σp² + σd²)), which is closest to the yield stress?
  5. Which method of strengthening steel raises the yield strength while also lowering the ductile-to-brittle transition temperature, improving toughness at low temperatures?