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Strengthening mechanisms and dislocations

Which method of strengthening steel raises the yield strength while also lowering the ductile-to-brittle transition temperature, improving toughness at low temperatures?

  1. AWork hardening by raising the dislocation density through cold work
  2. BSolid-solution strengthening by dissolved phosphorus or silicon
  3. CGrain refinement by controlled rolling and similar processes
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Answer: C. Grain refinement by controlled rolling and similar processes

Refining the grains raises the yield strength through the Hall–Petch relationship and, because cleavage cracks change direction or stop at grain boundaries, it also raises the stress needed to initiate and propagate cracks, so the ductile-to-brittle transition temperature falls. In steel the Hall–Petch coefficient is about 0.6 to 0.7 MPa·√m, larger than in aluminum or copper, so refinement is especially effective, and thermomechanical controlled processing (TMCP), in which steel containing Nb or Ti is rolled at low temperature and then accelerated-cooled, is widely used to strengthen steels for welded structures. Work hardening, precipitation strengthening and solid-solution strengthening by most elements other than Ni raise the yield strength but tend to raise the transition temperature and lower toughness. Phosphorus in particular segregates to grain boundaries and readily causes embrittlement.

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More Strengthening mechanisms and dislocations questions

  1. Strengthening a metal usually reduces its uniform elongation. Which statement correctly describes the idea behind TRIP and TWIP steels, which show large uniform elongation even at high strength? Assume that necking begins when dσ/dε = σ (σ and ε are true stress and true strain).
  2. Estimating the shear stress needed to displace the atomic planes above and below the slip plane all at once in a perfect crystal (the theoretical shear strength) as τ ≈ G/2π gives about 7.6 GPa for copper (shear modulus G = 48 GPa). Which is the correct reason why the shear stress at which a real copper single crystal begins to slip is orders of magnitude smaller, about 1 MPa?
  3. A single-crystal rod is pulled in tension. For a slip system whose slip-plane normal makes 60° and whose slip direction makes 40° with the tensile axis, the critical resolved shear stress is 0.80 MPa. Which is closest to the tensile stress at which this slip system begins to slip? Ignore other slip systems.
  4. The yield stress σy of an FCC polycrystal is about three times the critical resolved shear stress τc of a single crystal (σy ≈ Mτc, M ≈ 3.06). Which is the correct reason why this factor M (the Taylor factor) is larger than 2, the reciprocal of the maximum Schmid factor of 0.5?
  5. 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?