Fatigue Durability & Mechanical Reliability
Smith-Watson-Topper (SWT) & Morrow Fatigue Formula
Calculate Peak Cyclic Stress sigma_max = sigma_a + sigma_m, Smith-Watson-Topper Damage Stress SQRT(MAX(0, sigma_max) * epsilon_a * E), Morrow Mean-Stress Equivalent Amplitude, and Crack-Closure Regime.
Account for tensile crack opening and shot-peened compressive closure in strain-life fatigue!
Standard Coffin-Manson-Basquin strain-life curves are measured under fully reversed R = -1 zero-mean-stress cycling (sigma_m = 0). Superimposed tensile mean stress (sigma_m > 0) holds microcracks open and slashes fatigue life, whereas shot-peened compressive residual stress (sigma_m < 0) retards crack growth! Two canonical mean-stress corrections dominate SAE / automotive durability spreadsheets: (1) K.N. Smith, P. Watson, and T.H. Topper (1970, Journal of Materials) defined the energy-like Damage Stress Parameter P_SWT = SQRT(MAX(0, sigma_max) * epsilon_a * E), where sigma_max = sigma_a + sigma_m (automatically predicting zero propagating damage P_SWT = 0 whenever heavy compression keeps peak stress non-positive sigma_max <= 0!); and (2) JoDean Morrow (1968) reduced the fatigue strength coefficient sigma_f_prime by sigma_m, yielding Equivalent Fully Reversed Stress Amplitude sigma_ar_Morrow = sigma_a / (1 - sigma_m / sigma_f_prime)!
Verify on Stress_Amplitude sigma_a = 300 MPa (B2), Tensile_Mean_Stress sigma_m = 100 MPa (B3 -> Peak Stress sigma_max = 400.00 MPa in E2), Total_Strain_Amplitude epsilon_a = 0.0020 (B4), Youngs_Modulus E = 200 GPa (200,000 MPa, B5), and Fatigue_Strength_Coeff sigma_f_prime = 900 MPa (B6): SWT Equivalent Stress is SQRT(400 * 0.002 * 200,000) = SQRT(160,000) = 400.00 MPa (E3); Morrow Equivalent Reversed Stress is 300 / (1 - 100 / 900) = 337.50 MPa (E4); and Regime flags "Tensile Crack-Opening Penalty" (E5)!
| Strain-Life Mean-Stress Metric (sa=300, sm=+100 MPa, ea=0.002, E=200GPa, sf=900) | Formula | Verified Output |
|---|---|---|
| Peak Cyclic Stress sigma_max | sigma_a + sigma_m | 400.00 MPa (-50 MPa @ sm=-350) |
| SWT Damage Stress P_SWT (MPa) | SQRT(MAX(0, sigma_max) * ea * E_MPa) | 400.00 MPa (0.00 MPa @ sm=-350) |
| Morrow Equiv Reversed Stress | sigma_a / (1 - sigma_m / sigma_f_prime) | 337.50 MPa (216.00 MPa @ sm=-350) |
| Crack-Closure Loading Regime | sigma_max <= 0 vs sigma_m Sign | Tensile Crack-Opening Penalty |
Smith-Watson-Topper (SWT) Equivalent Damage Stress Formula
Validate sigma_a > 0, epsilon_a > 0, E_GPa > 0, and sigma_m < sigma_f_prime (if sigma_max <= 0 under heavy compressive clamping, MAX(0, sigma_max) prevents #NUM! inside SQRT and returns 0)!
=LET(sg_a, B2, sg_m, B3, ep_a, B4, md_e, B5, sf_p, B6, IF(OR(sg_a <= 0, ep_a <= 0, md_e <= 0, sf_p <= 0, sg_m >= sf_p), "Invalid Fatigue Cycle", LET(sg_x, sg_a + sg_m, ROUND(SQRT(MAX(0, sg_x) * ep_a * (md_e * 1000)), 2))))Shot-Peening Compressive Clamping Check (sigma_max <= 0)
Set Mean_Stress B3 = -350 MPa (shot-peened root): Peak Stress drops to -50 MPa, clamping SWT Damage Stress to 0.00 MPa while Morrow Equivalent Stress drops to 216.00 MPa!
=IF(ISTEXT(E3), E3, IF(E2 <= 0, "Compressive Crack Closure (SWT = 0)", IF(B3 > 0, "Tensile Crack-Opening Penalty", IF(B3 = 0, "Fully Reversed Baseline (R = -1)", "Compressive Mean Beneficial"))))Try the example
Use the original values or change them to test your understanding.