Strengthening mechanisms and dislocations
Learn about theoretical strength and dislocations, the Schmid and Taylor factors, the Peierls stress, solid-solution strengthening and the yield-point phenomenon, the Taylor equation, particle shearing and the Orowan mechanism, dispersion strengthening, superposition of strengthening and combining strength with ductility through multiple-choice questions.
Strengthening mechanisms and dislocations: key points
The strength of a metal is set by how hard it is for dislocations to move. In a single crystal, slip begins when the resolved shear stress on a slip system reaches the critical resolved shear stress, and its ratio to the tensile stress is given by the Schmid factor. In a polycrystal the grains must deform compatibly with one another, so the yield stress is the critical resolved shear stress multiplied by the Taylor factor (about 3 for FCC). In BCC metals the lattice resistance is large, and the yield stress depends strongly on temperature.
Strengthening methods can be classified by the kind of obstacle: solute atoms, other dislocations, precipitates and dispersed particles, and grain boundaries. Strengthening by dislocation density is estimated with the Taylor equation and strengthening by hard particles with the Orowan mechanism, while small precipitates are sheared by dislocations. Several contributions are combined by simple addition or by a root sum of squares. Most strengthening lowers ductility and toughness, but grain refinement and transformation or twinning during deformation open ways to combine strength with ductility and toughness.
All Strengthening mechanisms and dislocations questions (15)
- 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?
- 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.
- 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?
- 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?
- 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.
- 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?
- 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?
- 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)?
- 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.
- 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?
- 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?
- 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?
- 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?
- Which method of strengthening steel raises the yield strength while also lowering the ductile-to-brittle transition temperature, improving toughness at low temperatures?
- 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).