Different types of fatigue curves can be used for determining the fatigue strength of weld joints. The following are formulas for individual curves of normal and shear stress.
1. Method of virtual mean stress
where:
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σ a , τ a |
amplitude of normal (shear) stress [MPa, psi]. |
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σ e , τ e |
endurance limit at the constant strength [MPa, psi] |
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σ m , τ m |
mean cycle stress [MPa, psi]. |
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σ F , τ F |
virtual mean stress [MPa, psi]  |
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| Ψ |
factor of Haigh diagram narrowing [-] |
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depends on the joint material - recommended values - for traction and bending Ψ<0.15...0.3> |
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- for shear Ψ <0.1...0.25>. |
2. Modified Godman method
where:
|
σ a , τ a |
amplitude of normal (shear) stress [MPa, psi]. |
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|
σ e , τ e |
endurance limit at the constant strength [MPa, psi] |
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σ m , τ m |
mean cycle stress [MPa, psi]. |
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S U |
ultimate tensile strength [MPa, psi] |
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S US |
ultimate shear strength [MPa, psi] |
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while S US ≈ 0.8 S U |
3. Quadratic (Elliptic) method
for explanation of variables see the item 2 - Modified Godman method
4. Gerber parabolic method
for explanation of variables see the item 2 - Modified Godman method
5. Method by Keccecioglu, Chester, and Dodge
where:
|
σ a , τ a |
amplitude of normal (shear) stress [MPa, psi]. |
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|
σ e , τ e |
endurance limit at the constant strength [MPa, psi] |
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σ m , τ m |
mean cycle stress [MPa, psi]. |
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S U |
ultimate tensile strength [MPa, psi] |
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S US |
ultimate shear strength [MPa, psi] |
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while S US ≈ 0.8 S U |
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a |
exponent depending on the joint material [-] |
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recommended values a <2.6...2.75> |
6. Method by Bagci
where:
|
σ a , τ a |
amplitude of normal (shear) stress [MPa, psi]. |
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|
σ e , τ e |
endurance limit at the constant strength [MPa, psi] |
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σ m , τ m |
mean cycle stress [MPa, psi]. |
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S Y |
yield tensile strength [MPa, psi] |
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S YS |
yield shear strength [MPa, psi] |
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while S YS ≈ 0.577 S Y |
7. Soderberg Method
for explanation of variables see the item 6 - Method by Bagci