Adjust initial crack size, stress range, and material constants to compute the crack growth curve, critical crack size, and remaining fatigue life — all in your browser.
So, what exactly is "fatigue crack growth"? If a material doesn't break immediately, how does a crack get bigger over time?
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Basically, it's the slow, progressive extension of a tiny flaw under repeated, or cyclic, loading. Think of bending a paperclip back and forth—it doesn't snap on the first bend, but a small crack forms and grows with each cycle until failure. In this simulator, you control the starting crack size (a₀) and the cyclic Stress range Δσ to see this process unfold.
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Wait, really? So there's a mathematical law that predicts this growth? What do the C and m sliders actually represent?
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Exactly! That's the Paris Law. The sliders C and m are material constants you can experiment with. C is like the baseline growth rate, and m is the exponent that controls how sensitive the growth is to stress. For instance, aluminum has a different pair of values than steel. Try setting a high m value and watch how the crack growth curve on the graph becomes much steeper.
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That makes sense. But when does it become dangerous? How does the simulator know when the part will fail?
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Great question! That's where Fracture toughness K_Ic comes in. It's a material property that tells us the maximum stress intensity the material can withstand. The simulator calculates a "critical crack size" (a_c). When the growing crack reaches that size, failure is imminent. Adjust the K_Ic parameter and see how the vertical failure line on the plot moves, changing the component's remaining life dramatically.
Physical Model & Key Equations
The core model is the Paris Law, which governs the crack growth rate per load cycle. The driving force is the Stress Intensity Factor Range, ΔK.
$$\frac{da}{dN}= C(\Delta K)^m$$
da/dN: Crack growth per cycle (m/cycle) C: Paris constant, material-dependent (m/cycle) m: Paris exponent, material-dependent ΔK: Range of the stress intensity factor (MPa√m)
The stress intensity factor range ΔK depends on the applied stress, current crack size, and the geometry of the component. For a central crack in a finite-width plate, we use the following:
$$\Delta K = \Delta\sigma \cdot Y\sqrt{\pi a}\quad \text{where}\quad Y = \sqrt{\sec\left(\frac{\pi a}{2W}\right)}$$
Δσ: Applied stress range (MPa) = σ_max - σ_min a: Current crack length (m) W: Width of the plate (m) Y: Geometry correction factor (accounts for finite width)
Frequently Asked Questions
C and m are material-specific values determined from experimental data. Reference values for common metallic materials can be found in literature or material databases. In this simulator, representative values for aluminum alloy (C=1e-11, m=3) are set as defaults, but please modify them according to the analysis target.
No, this simulator calculates only the propagation behavior and residual life up to the point where the crack reaches the critical size (the input critical crack length) based on Paris' law. Rapid fracture after the critical point and fracture surface analysis are not covered. Please use it solely as a tool for predicting fatigue crack propagation life.
Since Paris' law is based on linear elastic fracture mechanics, if the stress amplitude is too large, the plastic zone at the crack tip becomes non-negligible, exceeding the applicable range. As a guideline, if the maximum stress exceeds 30% of the material's yield stress, the accuracy of the results decreases. In such cases, consider applying elastic-plastic fracture mechanics.
Feddersen's correction formula (sec function) is used as the exact solution for a center crack in a finite-width plate. This formula accurately represents the effect of accelerated crack growth as the ratio of crack length to plate width increases (finite width correction). If you wish to analyze other geometries, please replace it with the corresponding Y formula.
Real-World Applications
Aircraft Structural Inspection: Engineers use Paris Law to predict the "safe life" of critical components like wing spars or landing gear. By knowing the initial flaw size from inspections and the flight load cycles, they schedule maintenance before a crack reaches the critical size, preventing catastrophic failure.
Bridge and Infrastructure Monitoring: Steel bridges experience daily stress cycles from traffic and wind. Fatigue analysis helps determine inspection intervals for weld details and connections, ensuring cracks are detected and repaired long before they compromise structural integrity.
Automotive and Railway Axles: Rotating components like axles are subjected to fully reversed bending stresses. Predicting fatigue crack growth is essential for designing these parts for a specific lifespan, balancing safety with material cost and weight.
Energy Sector (Wind Turbines, Pipelines): Wind turbine blades undergo billions of cyclic loads. Pipeline welds experience pressure fluctuations. Applying Paris Law allows for a damage-tolerant design philosophy, where the presence of cracks is acknowledged and managed through planned inspections throughout the asset's life.
Common Misconceptions and Points to Note
When starting with this simulator, there are several pitfalls that beginners in CAE often encounter. First is the point that "Paris' Law is not a universal solution". This law holds well in the intermediate region of crack growth (so-called "Region II"), but different models are needed for the very slow growth region (the threshold) and the high-speed region just before fracture. It is dangerous to trust the simulator's results as an absolute life estimate; please consider them as a guideline only.
Next, the importance of setting the initial crack size a₀. For example, calculating with a₀ as 0.1mm versus 1mm can change the remaining life by several times. In practice, the minimum size detectable by non-destructive testing is often used for a₀. Be careful not to set a₀ extremely small under the assumption that "there should be no flaw," as this will yield an unrealistically optimistic life prediction.
Finally, the reality that "the stress range Δσ is not constant". While the simulator uses a fixed value, actual machinery and structures experience loads of varying magnitudes applied randomly. For such variable amplitude loading, cumulative damage calculations, such as using Miner's rule in combination, become necessary. Once you've learned the basics with this tool, handling this "load history" becomes the next practical challenge.