Coffin-Manson & Basquin Strain-Life Fatigue Equation + Transition Life (2Nt)

Unify low-cycle plastic yielding and high-cycle elastic fatigue!

Turbine disks, pressure-vessel nozzles, and notched shafts experience local plastic strain during thermal startups and overloads where stress-life S-N curves break down! The total strain-life equation adds Basquin's elastic strain amplitude (sigma_f' / E) * (2Nf)^b and Coffin-Manson's plastic strain amplitude epsilon_f' * (2Nf)^c: delta_epsilon / 2 = (sigma_f' / E) * (2Nf)^b + epsilon_f' * (2Nf)^c, where 2Nf is the number of load reversals (2 reversals = 1 full cycle)!

Setting elastic and plastic strain amplitudes equal solves analytically for the transition fatigue life 2Nt = ((epsilon_f' * E) / sigma_f') ^ (1 / (b - c))! Below 2Nt reversals, plastic ductility epsilon_f' governs low-cycle fatigue (LCF); above 2Nt reversals, fatigue strength sigma_f' governs high-cycle fatigue (HCF). For alloy steel (sigma_f' = 950 MPa, E = 200,000 MPa, b = -0.09, epsilon_f' = 0.55, c = -0.56), at 2Nf = 1,000 reversals total strain amplitude is 0.01404 (1.404%), and transition life occurs at 2Nt = 24,591.5 reversals!

Total Strain Amplitude delta_epsilon / 2 (Basquin + Coffin-Manson)

Evaluates elastic plus plastic strain amplitude for target reversals 2Nf in B7.

=IF(OR(B2 <= 0, B3 <= 0, B5 <= 0, B7 <= 0, B4 >= 0, B6 >= 0), "Invalid Fatigue Parameters", ROUND(((B2 / B3) * (B7 ^ B4)) + (B5 * (B7 ^ B6)), 5))

Transition Fatigue Life in Reversals (2Nt)

Solves ((epsilon_f' * E) / sigma_f') ^ (1 / (b - c)) for the exact LCF-to-HCF crossover reversals.

=IF(OR(B2 <= 0, B3 <= 0, B5 <= 0, B4 = B6), "Invalid Fatigue Parameters", ROUND(((B5 * B3) / B2) ^ (1 / (B4 - B6)), 1))

Further reading

• Microsoft Support — POWER function