Enter bolt grade, nominal diameter, joint stiffness ratio, and external load to compute preload, working stresses, and fatigue safety factor. The Goodman diagram updates in real time with your operating point.
What exactly is "bolt fatigue," and why is it such a big deal in engineering?
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Basically, it's when a bolt fails from repeated, fluctuating loads, not from a single massive overload. Think of bending a paperclip back and forth until it snaps. In practice, this is a major cause of failure in everything from car engines to wind turbines. That's why we use standards like VDI 2230 to design against it.
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Wait, really? So the initial tightening force matters for fatigue? I thought you just make it "tight enough."
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Absolutely! A high, controlled preload is your best defense. It keeps the joint clamped so the bolt carries only a small fraction of the external load. Try moving the "External Load Fa" slider up in the simulator. See how the "Bolt Force Fb,max" increases? A good preload (Fi) makes that increase much smaller, which directly reduces the stress fluctuation that causes fatigue.
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That makes sense. So what's this "Stiffness Ratio Φ" parameter? It sounds abstract.
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It's the heart of the load distribution! In simple terms, it's the fraction of the external load that the bolt "feels." If Φ is 0.1, and you apply a 1000 N external load, the bolt force only increases by 100 N. Change the Φ value in the tool and watch the "Bolt Force" change. A common case is a bolt connecting a stiff flange (low Φ) versus a soft gasket (high Φ).
Physical Model & Key Equations
The analysis follows the VDI 2230 guideline. First, we calculate the maximum permissible preload during assembly, which is limited by the bolt's yield strength and the uncertainty in tightening.
$$F_i = \frac{0.7\,R_{p0.2}\,A_s}{\alpha_A}$$
Fi = Maximum assembly preload [N] Rp0.2 = Bolt material yield strength [MPa] (depends on Bolt Grade) As = Bolt stress area [mm²] (depends on Nominal Diameter d) αA = Tightening factor (≥ 1.0). Accounts for tool scatter (e.g., 1.4 for manual wrench, 1.2 for torque wrench).
Under operation, the bolt experiences a force range. The key fatigue parameter is the alternating stress in the bolt, which is compared to the bolt's endurance limit.
Fb,max = Maximum bolt force in operation [N] Φ = Stiffness ratio (load factor). Dictates how much external load (Fa) the bolt carries. σa = Alternating stress amplitude [MPa]. The driving force for fatigue. σASV = Permissible stress amplitude [MPa]. The bolt's fatigue strength, considering thread notch, surface, and size effects. SB = Fatigue safety factor. Must be > 1.0 for a safe design.
Frequently Asked Questions
α_A is a coefficient representing the variation of the tool used. For a torque wrench, a guideline is 1.4 to 1.6, and for a hydraulic wrench, 1.1 to 1.3. If there is no actual measurement data, a value of 1.6 is recommended on the safe side.
First, increase the strength grade of the bolt (e.g., from 10.9 to 12.9), then increase the nominal diameter, or lower the stiffness ratio Φ (increase the stiffness of the clamped parts) to move the operating point into the safe region.
It mainly supports JIS standard strength grades from 4.6 to 12.9. The yield strength Rp0.2 is automatically set for each grade, but if you want to input a custom material, you can also specify the yield strength directly.
In principle, fatigue failure does not occur under constant load alone, but in actual machines, stress fluctuations due to minute vibrations or temperature changes may occur. For safety, it is recommended to input 5 to 10% of the external load as a fluctuating component and evaluate it.
Real-World Applications
Automotive Engine Cylinder Heads: Hundreds of bolts clamp the head to the engine block, sealing high-pressure combustion gases. They undergo massive thermal cycles and pressure pulses. Fatigue analysis ensures they last the life of the vehicle without loosening or snapping.
Wind Turbine Flange Connections: The massive bolts connecting tower sections are subjected to constantly changing bending moments from wind gusts. A fatigue failure here would be catastrophic, so precise preload and high fatigue safety factors are critical.
Aerospace Structural Joints: In aircraft frames, weight is paramount. Engineers use high-strength bolts (like Grade 12.9) and optimize preload to minimize bolt size while surviving decades of pressurization cycles and turbulence-induced vibrations.
Heavy Machinery & Press Frames: The bolts in a stamping press frame experience shock loads every cycle. Fatigue analysis prevents unexpected downtime and dangerous failures in an industrial setting, ensuring the joint remains rigid under impact.
Common Misconceptions and Points to Note
When starting to use this tool, there are several pitfalls that beginners in CAE, in particular, often fall into. The first is the idea that selecting a bolt with a higher strength class solves everything. While it's true that high-strength bolts like 10.9 or 12.9 have high static strength, their fatigue strength is heavily influenced by surface condition and notch sensitivity. For example, even within the same 12.9 class, an untreated surface is more susceptible to fatigue crack propagation from micro-flaws, risking an overestimation of the safety factor. When you change the strength class in the tool, make it a habit to always check the datasheet and ask, "Is this the bolt's true fatigue limit?"
The second is confusing the stiffness ratio Φ and the tightening factor α_A. Φ is a parameter determined by "design" (the shape and material of the clamped parts). On the other hand, α_A is a coefficient determined by "workmanship" (is it an impact wrench or torque wrench? What's the skill level?). For instance, even with an excellent design of Φ=0.2, if you set α_A from the default 1.2 to 1.6 (indicating high workmanship variation), the initial clamping force F_i decreases, shifting the operating point towards the danger zone. It's crucial to consider "design parameters" and "workmanship parameters" separately and to set α_A to a value that reflects your actual assembly environment.
The third is over-reliance on the "safe side" interpretation of the Goodman diagram. The fatigue safety factor calculated by the tool is ultimately a theoretical value based on data for smooth materials (without notches). Real bolts have the thread root as a major stress concentrator. Even if the safety factor exceeds 1.5, unexpected early failure can occur if the R (surface roughness) at the thread root is poor. You should view this tool's output as a "first-step screening"; for critical joints, it's always necessary to verify with detailed CAE that considers local stresses at the thread or with actual durability tests.
Select bolt diameter (dSlider) from 6mm to 36mm and grade (phiVal) such as 8.8, 10.9, or 12.9
Enter axial working load (faVal) in kN and alternating load amplitude (aaVal) in kN
Review preload Fi, maximum bolt force Fb_max, stress amplitude σa, and mean stress σm; fatigue safety factor updates automatically based on Goodman or Haigh criterion
Worked Example
M16 ISO 8.8 bolt (diameter 16mm, yield 640 MPa) with initial preload 65 kN, static load 40 kN, alternating amplitude 15 kN: Fi=65kN, Fb_max=120kN, σa=73.5 MPa, σm=298 MPa, resulting fatigue safety factor 2.1 against 10⁷ cycle endurance limit of 160 MPa (grade 8.8). Increasing bolt grade to 10.9 (yield 900 MPa, endurance 220 MPa) raises safety factor to 3.0.
Practical Notes
Preload should be 50–70% of proof load; excessive preload (>80%) causes joint relaxation and reduced fatigue life in vibration-prone applications like automotive suspension mounts
Joint stiffness ratio km/kb affects load distribution; stiffer clamped parts (km higher) shift more alternating load to bolt, lowering safety factor
Corrosion reduces fatigue strength by 20–35%; use cadmium or zinc-nickel plating for marine/chemical environments
Stress concentration factor Kt from surface finish and thread roots is embedded in grade endurance limits; rolled threads outperform cut threads by 10–15%