Below the yield point, bonds stretch reversibly and strain is
proportional to stress (Hooke's law). Past yield, dislocations glide
through the lattice — visualized as a slipped row of atoms — and strain
grows permanently until bonds snap at the fracture stress.
σ = E·ε (elastic region, E = Young's modulus)
σ_yield ↓ as T↑ and defect density↑
fracture when σ ≥ σ_yield·(1 + hardening) and ε > ε_crit
- Applied stress — the tensile load pulling the lattice apart, in MPa.
- Temperature — higher temperature softens bonds and lowers the yield point, mimicking thermal weakening.
- Defect density — vacancies and impurities that make dislocations easier to nucleate, lowering yield strength further.
This elastic → plastic → fracture sequence is exactly what a
real tensile-test stress-strain curve captures, and it's the basis
for every material safety factor an engineer specifies.