PRINCIPLES OF COMPOSITE MATERIAL
MECHANICS 4TH EDITION GIBSON
SOLUTIONS MANUAL FINAL PAPER 2026
COMPLETE SOLUTIONS AND CORRECT
ANSWERS GRADED A+
⩥ the yield strength is proportional to ______ of grain size. Answer: the
inverse square root
⩥ least affected lattice structure to most affected lattice structure: for
grain size strengthening. Answer: FCC, HCP, BCC
⩥ hall-petch relation for nanocrystalline materials. Answer: they have a
large volute of GB regions, and can achieve much higher stresses
⩥ ___% of atoms in nanocrystalline materials are in the grain boundary.
Answer: 40
⩥ solid solution. Answer: alloy with solute atoms within range of solid
solubility occupying either substitutional or interstitial sites
⩥ the effect of dislocation interactions with solute atoms depends on (2).
Answer: a. symmetric misfit strain (size difference in sub atoms)
, b. type of interstitial site (symmetric FCC< non-symmetric BCC)
⩥ Hume-Rothery rules (4). Answer: Materials can form a solid solution
IF
1. The atomic radius of the solute and solvent atoms must differ by no
more than 15%
2. The crystal structures of solute and solvent must be similar.
3. Complete solubility occurs when the solvent and solute have the same
valency. A metal is more likely to dissolve a metal of higher valency,
than vice versa
4. should have similar electronegativity
⩥ interstitial atom sites in FCC. Answer: symmetric
- octahedral in center of FCC
- tetrahedral on side
⩥ interstitial atom sites in bcc. Answer: non-symmetric
- nonsymmetric octahedral in center of face in BCC
- non-symmetric tetrahedral
⩥ substitution interaction energy. Answer: small
F≈ Gb²/120
MECHANICS 4TH EDITION GIBSON
SOLUTIONS MANUAL FINAL PAPER 2026
COMPLETE SOLUTIONS AND CORRECT
ANSWERS GRADED A+
⩥ the yield strength is proportional to ______ of grain size. Answer: the
inverse square root
⩥ least affected lattice structure to most affected lattice structure: for
grain size strengthening. Answer: FCC, HCP, BCC
⩥ hall-petch relation for nanocrystalline materials. Answer: they have a
large volute of GB regions, and can achieve much higher stresses
⩥ ___% of atoms in nanocrystalline materials are in the grain boundary.
Answer: 40
⩥ solid solution. Answer: alloy with solute atoms within range of solid
solubility occupying either substitutional or interstitial sites
⩥ the effect of dislocation interactions with solute atoms depends on (2).
Answer: a. symmetric misfit strain (size difference in sub atoms)
, b. type of interstitial site (symmetric FCC< non-symmetric BCC)
⩥ Hume-Rothery rules (4). Answer: Materials can form a solid solution
IF
1. The atomic radius of the solute and solvent atoms must differ by no
more than 15%
2. The crystal structures of solute and solvent must be similar.
3. Complete solubility occurs when the solvent and solute have the same
valency. A metal is more likely to dissolve a metal of higher valency,
than vice versa
4. should have similar electronegativity
⩥ interstitial atom sites in FCC. Answer: symmetric
- octahedral in center of FCC
- tetrahedral on side
⩥ interstitial atom sites in bcc. Answer: non-symmetric
- nonsymmetric octahedral in center of face in BCC
- non-symmetric tetrahedral
⩥ substitution interaction energy. Answer: small
F≈ Gb²/120
