Fatigue Life Calculator
Estimate fatigue life using S-N curve data and Miner rule for cumulative damage. Enter values for instant results with step-by-step formulas.
Formula
Se = ka x kb x kc x Sf | Goodman: Sa/(1 - Sm/Su) | D = n/Nf
The modified endurance limit Se is the fatigue strength adjusted by Marin surface (ka), size (kb), and reliability (kc) factors. The Goodman criterion converts mean+alternating stress to equivalent fully-reversed stress. Miner's rule accumulates damage as the ratio of applied to allowable cycles.
Worked Examples
Example 1: Steel Shaft Under Reversed Bending
Problem: A machined steel shaft (Su = 500 MPa, Sf = 250 MPa) experiences 250 MPa alternating stress with 50 MPa mean stress. Surface factor 0.85, size factor 0.90, reliability 0.897. Estimate fatigue life.
Solution: Modified Se = 250 x 0.85 x 0.90 x 0.897 = 171.7 MPa\nGoodman equivalent = 250 / (1 - 50/500) = 277.8 MPa\nSince 277.8 > 171.7 MPa, finite life expected\nUsing S-N approach with slope from 0.9 x Su at 10^3 to Se at 10^6\nlog(450) = 2.653, log(171.7) = 2.235\nSlope m = (2.653 - 2.235) / (3 - 6) = -0.139\nFatigue life estimated from S-N relationship
Result: Finite life predicted | Goodman SF = 0.618 | Component operates above endurance limit
Example 2: Cumulative Damage Assessment
Problem: The same shaft has already experienced 100,000 load cycles. Assess remaining life using Miner's rule if S-N life is 500,000 cycles.
Solution: Applied cycles: 100,000\nS-N life at operating stress: 500,000 cycles\nDamage fraction D = 100,000 / 500,000 = 0.20 (20%)\nRemaining life = 1 - 0.20 = 0.80 (80%)\nRemaining cycles = 0.80 x 500,000 = 400,000 cycles
Result: Damage: 20% | Remaining life: 80% (400,000 cycles remaining)
Frequently Asked Questions
What is fatigue life and why is it important in engineering?
Fatigue life is the number of stress cycles a material or component can withstand before failure occurs due to progressive and localized structural damage from cyclic loading. Unlike static failure where a single overload causes fracture, fatigue failure occurs at stress levels well below the material's ultimate tensile strength or even yield strength. Fatigue is responsible for approximately 80 to 90 percent of all structural failures in engineering applications, making it the most critical failure mode in mechanical design. Components subject to repeated loading such as aircraft wings, bridge structures, engine crankshafts, turbine blades, and automotive suspension parts must be designed with fatigue considerations. The fatigue design process involves characterizing the loading spectrum, determining material fatigue properties from S-N curves, applying mean stress corrections, and incorporating safety factors to ensure reliable service life.
How does the S-N curve characterize material fatigue behavior?
The S-N curve (stress-life curve or Wohler curve) plots stress amplitude versus the number of cycles to failure on a log-log scale. It is the fundamental characterization tool for fatigue analysis. For ferrous metals like steel, the curve typically shows a distinct knee point around 10 to the sixth to 10 to the seventh cycles, below which the material theoretically has infinite life. This stress level is called the endurance limit or fatigue limit. For non-ferrous metals like aluminum and copper alloys, there is no true endurance limit and the curve continues to decrease. The S-N curve is obtained through rotating beam or axial fatigue testing of multiple specimens at different stress levels, recording cycles to failure. The high-cycle fatigue region (greater than 10 to the fourth cycles) is primarily elastic and stress-controlled, while low-cycle fatigue involves significant plastic deformation and is strain-controlled.
What is Miner's rule for cumulative fatigue damage?
Miner's rule, also known as the Palmgren-Miner linear damage accumulation rule, states that fatigue damage from different stress levels can be summed linearly. The damage fraction at each stress level equals the ratio of applied cycles to the cycles-to-failure at that stress level: D = sum of (ni / Nfi). Failure is predicted when the total damage D reaches 1.0 (100 percent). For example, if a component experiences 50,000 cycles at a stress level that would cause failure at 200,000 cycles, the damage is 0.25 or 25 percent, leaving 75 percent remaining life. While widely used for its simplicity, Miner's rule has known limitations: it does not account for load sequence effects (high-then-low versus low-then-high loading produces different results), it ignores crack initiation versus propagation differences, and experimental data shows failure at damage sums ranging from 0.7 to 2.2.
How accurate are the results from Fatigue Life Calculator?
All calculations use established mathematical formulas and are performed with high-precision arithmetic. Results are accurate to the precision shown. For critical decisions in finance, medicine, or engineering, always verify results with a qualified professional.
Can I use the results for professional or academic purposes?
You may use the results for reference and educational purposes. For professional reports, academic papers, or critical decisions, we recommend verifying outputs against peer-reviewed sources or consulting a qualified expert in the relevant field.
Can I use Fatigue Life Calculator on a mobile device?
Yes. All calculators on NovaCalculator are fully responsive and work on smartphones, tablets, and desktops. The layout adapts automatically to your screen size.