Strengthening Mechanisms in Metals/Alloys

Abstract

Mechanical engineers and material technologists often face challenges to design and develop materials with greater strength for highly-stressed applications. These challenging technological environments demand controlled strengthening of alloys by using appropriate strengthening mechanisms. This chapter first introduces the significance of dislocation motions in strengthening of a metal/alloy. Then various strengthening mechanisms have been discussed and mathematically modeled; the main topics include: grain boundary strengthening, strain/work hardening, solid solution strengthening, precipitation strengthening, and dispersion strengthening. This chapter contains 11 diagrams and 10 worked examples/solved problems, 7 exercise problems, 7 mathematical formulae, and 5 MCQs with their answers at the end of the book.

Questions and Problems

• 4.1. (MCQs). Underline the most appropriate answers for each of the following questions:

  • (a) Which type of strengthening requires a higher stress to cross an array of dislocations?

    (i) strain hardening, (ii) grain-boundary strengthening, (iii) solid solution strengthening.

  • (b) Which type of strengthening requires a greater stress to move a dislocation through the large number of intermingled dislocations?

    (i) strain hardening, (ii) grain-boundary strengthening, (iii) precipitation strengthening.

  • (c) Which type of strengthening is achieved by the presence of coherent precipitates?

    (i) dispersion strengthening, (ii) solid-solution hardening, (iii) precipitation strengthening.

  • (d) Which type of strengthening is achieved by the presence of non-coherent precipitates?

    (i) dispersion strengthening, (ii) strain hardening, (iii) precipitation strengthening.

  • (e) Which type of strengthening results to stress field caused by the presence of solute atoms?

    (i) strain hardening, (ii) solid-solution hardening, (iii) precipitation strengthening

• 4.2. Explain the role of dislocation movements in plastic deformation of a solid with the aid of sketches.

• 4.3. (a) What is the basic principle of strengthening mechanism?

  (b) List the various strengthening mechanisms, and explain any of them.

• 4.4. (a) Why is an alloy generally stronger than pure metal?

  (b) Draw diagrams showing interstitial solid solution and substitutional solid solutions.

  (c) Why is strengthening by dissolving carbon in BCC iron is more pronounced as compared to dissolving carbon in FCC iron?

• 4.5. Explain grain-boundary strengthening with the aid of diagram(s).

• 4.6. Explain strain hardening with reference to dislocation density.

• 4.7. Draw diagrams illustrating coherent precipitates and non-coherent precipitate.

• 4.8. Differentiate between precipitation strengthening and dispersion strengthening, giving examples for each type of strengthening.

• 4.9. The yield strength of a sample of annealed aluminum with an average grain size of 0.037 mm is 36 MPa. The yield strength of a single-crystal sample of the metal is σ₀ = 25 MPa. Calculate the yield strength of a sample of aluminum with average grain size of 0.05 mm.

• 4.10. Refer to Fig. 4.4. What is the average grain diameter (in nanometer) of cryo-milled aluminum that corresponds to the highest yield strength in the graphical plot?

• 4.11. By using the data in Problem 4.10, draw a graphical plot for ${d}^{-\frac{1}{2}}$ versus σ_ys; and hence graphically determine the constants K and σ₀ in the Hall-Petch relationship for the metal.

• 4.12. An etched sample of a strain-hardened metal contains 10⁷etch pits (dislocations) in a 3 mm² area. What is the dislocation density in the metal sample?

• 4.13. A precipitation-strengthened nickel-base alloy’s microstructure comprises of FCC γ phase (matrix) and the precipitated γ^′ phase having a lattice parameter of 0.3568 nm. Calculate the percent lattice mismatch. Nickel (FCC lattice) has the atomic radius of 0.1246 nm

• 4.14. By using the data in Problem 4.11, calculate the flow stress of the metal. The constants for the flow stress-dislocation density relation are: k = 1.7 x 10⁻³ MPa-cm and σ₀ = 0.05 MPa.

• 4.15. A 5-mm-thick sheet made of made of AISI 304 N ASS is cold rolled to 3.5-mm thickness with no change in width. Determine the tensile mechanical properties of the steel.