300
MPa
1
59,049
29,525
4.47
0.03
million cycles
300
MPa
1
59,049
29,525
4.47
0.03
million cycles
The Fatigue Life Calculator estimates the number of cycles to failure under cyclic loading using the Basquin equation (stress-life approach), the foundational relationship in high-cycle fatigue analysis:
$$\sigma_a = \sigma'_f \, (2N_f)^b$$
Solving for the number of cycles to failure: $$N_f = \frac{1}{2} \left(\frac{\sigma_a}{\sigma'_f}\right)^{1/b}$$
where $$\sigma_a$$ is the stress amplitude (half the stress range), $$\sigma'_f$$ is the fatigue strength coefficient (approximately equal to the true fracture stress), $$b$$ is the fatigue strength exponent (typically −0.05 to −0.15 for metals), and $$2N_f$$ is the number of reversals to failure (one cycle = two reversals).
For loading with non-zero mean stress, the calculator applies the Goodman correction to compute an equivalent fully-reversed stress amplitude: $$\sigma_{ar} = \frac{\sigma_a}{1 - \sigma_m / \sigma_{uts}}$$ where $$\sigma_m$$ is the mean stress and $$\sigma_{uts}$$ is the ultimate tensile strength. This corrected amplitude is then used in the Basquin equation. Fatigue life prediction is essential in aerospace, automotive, civil, and mechanical engineering where components experience millions of load cycles during their service life.
The stress-life (S-N) approach characterizes fatigue behavior by plotting stress amplitude versus cycles to failure on log-log axes. The Basquin equation describes the linear region of this S-N curve:
$$\sigma_a = \sigma'_f \, (2N_f)^b$$
Key parameters and their physical meaning:
The Goodman diagram accounts for the effect of mean stress on fatigue life. Tensile mean stress reduces fatigue life; compressive mean stress can increase it. The Goodman relation is conservative and widely used in design: $$\frac{\sigma_a}{\sigma_{ar}} + \frac{\sigma_m}{\sigma_{uts}} = 1$$
Rearranging: $$\sigma_{ar} = \frac{\sigma_a}{1 - \sigma_m/\sigma_{uts}}$$
This equivalent amplitude $$\sigma_{ar}$$ is then substituted into the Basquin equation to find the adjusted fatigue life. Other mean stress corrections exist (Gerber, Soderberg, Morrow), each with different conservatism levels.
The stress-life approach is most suitable for high-cycle fatigue ($$N_f > 10^4$$ cycles) where deformation is predominantly elastic. For low-cycle fatigue with significant plastic strain, the strain-life approach (Coffin-Manson equation) is more appropriate.
The cycles to failure $$N_f$$ represents the expected fatigue life under constant-amplitude loading. In design practice, apply a safety factor of 2–10 on life or 1.5–2 on stress depending on the application criticality. High-cycle fatigue ($$N_f > 10^6$$) typically occurs below the yield strength; low-cycle fatigue ($$N_f < 10^4$$) involves plastic deformation. The mean stress effect is significant: a tensile mean stress of half the UTS roughly halves the allowable stress amplitude. For variable-amplitude loading, Miner's rule ($$\sum n_i/N_{f,i} = 1$$) provides a first-order life estimate.
Inputs
Results
At 300 MPa fully-reversed stress amplitude with σ'f = 900 MPa and b = −0.1, the predicted life is about 29,500 cycles. With zero mean stress, the Goodman correction has no effect.
Inputs
Results
Without mean stress, Nf ≈ 43 million cycles. The Goodman correction with 150 MPa mean stress raises the equivalent amplitude to 254.5 MPa, reducing life to about 5.0 million cycles — an order of magnitude reduction.
The Basquin equation $$\sigma_a = \sigma'_f (2N_f)^b$$ is an empirical relationship that describes the linear portion of the stress-life (S-N) curve on log-log axes. Published by O.H. Basquin in 1910, it relates the stress amplitude to the number of reversals to failure using two material constants: the fatigue strength coefficient $$\sigma'_f$$ and the fatigue strength exponent $$b$$.
The fatigue strength exponent $$b$$ is the slope of the S-N curve on a log-log plot. It is always negative (fatigue life decreases with increasing stress). Typical values for metals range from −0.05 (excellent fatigue resistance) to −0.15 (poor fatigue resistance). Most structural steels have $$b \approx -0.08$$ to $$-0.12$$.
Tensile mean stress reduces fatigue life by opening cracks more during each cycle. The Goodman equation accounts for this: $$\sigma_{ar} = \sigma_a / (1 - \sigma_m/\sigma_{uts})$$. At a mean stress of half the UTS, the equivalent amplitude doubles, dramatically reducing life. Compressive mean stress generally improves fatigue life, which is why shot peening (introducing compressive residual stress) is widely used.
High-cycle fatigue (HCF, $$N_f > 10^4$$–$$10^5$$) occurs at stress levels below the yield strength where deformation is elastic — the Basquin equation applies. Low-cycle fatigue (LCF, $$N_f < 10^4$$) involves significant plastic strain each cycle — the Coffin-Manson equation (strain-life approach) is needed. Many components experience both regimes during different loading conditions.
A cycle is one complete loading sequence from minimum to maximum and back to minimum stress. A reversal is a half-cycle — from one extreme to the other. Thus $$2N_f$$ reversals = $$N_f$$ cycles. The Basquin equation is traditionally written in terms of reversals, but this calculator converts to cycles for practical interpretation.
For constant-amplitude loading under controlled conditions, the Basquin equation typically predicts fatigue life within a factor of 2–3. In real service, scatter factors of 10 or more are common due to surface finish, residual stresses, environmental effects, manufacturing defects, and variable-amplitude loading. Design codes apply safety factors accordingly — typically 4 on life or 1.5 on stress.
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