Materials & Fatigue — Cheat Sheet

Stress-strain, elastic constants, endurance limit, hardness relations.

σa σm Se Sut load point failure line safe
Goodman diagram — any load point below the line survives indefinitely.

Elastic behaviour

Hooke (axial)σ = E·ε
Shearτ = G·γ
E-G-ν relationG = E / [2(1+ν)]
Poissonε_lat = −ν·ε_axial
Bulk modulusK = E / [3(1−2ν)]

Strength & safety

Factor of safetyn = S_y / σ
Ultimate vs yieldS_ut > S_y
True stressσ_t = σ(1 + ε)

Fatigue

Endurance limitSe' = 0.5·S_ut (steel, ≤1400 MPa)
CorrectedS_e = k_a k_b k_c k_d k_e · Se
Goodmanσ_a/S_e + σ_m/S_ut = 1/n
Notch factorK_f = 1 + q(K_t − 1)

Handy relations

Hardness→tensileS_ut(MPa) ≈ 3.45·HB
Thermal stressσ = E·α·ΔT
Stiffnessk = AE/L (axial)

Formula reference — verify against the governing standard. Not a substitute for engineering judgment.