Materials & Fatigue — Cheat Sheet
Stress-strain, elastic constants, endurance limit, hardness relations.
Goodman diagram — any load point below the line survives indefinitely.
Elastic behaviour
| Hooke (axial) | σ = E·ε |
| Shear | τ = G·γ |
| E-G-ν relation | G = E / [2(1+ν)] |
| Poisson | ε_lat = −ν·ε_axial |
| Bulk modulus | K = E / [3(1−2ν)] |
Strength & safety
| Factor of safety | n = S_y / σ |
| Ultimate vs yield | S_ut > S_y |
| True stress | σ_t = σ(1 + ε) |
Fatigue
| Endurance limit | Se' = 0.5·S_ut (steel, ≤1400 MPa) |
| Corrected | S_e = k_a k_b k_c k_d k_e · Se |
| Goodman | σ_a/S_e + σ_m/S_ut = 1/n |
| Notch factor | K_f = 1 + q(K_t − 1) |
Handy relations
| Hardness→tensile | S_ut(MPa) ≈ 3.45·HB |
| Thermal stress | σ = E·α·ΔT |
| Stiffness | k = AE/L (axial) |
Formula reference — verify against the governing standard. Not a substitute for engineering judgment.