Corrected endurance limit at the constant strength σ e or τ e of the bolted connection is determined for the selected type, design, material, and joint loading from the formula:
σ e = σ' e k a k b k c k d k e k f [MPa, psi]
where:
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σ' e |
basic endurance limit of a test bar from the selected material [MPa, psi]. |
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k a |
surface factor [-]. |
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k b |
size factor [-]. |
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k c |
reliability factor [-]. |
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k d |
operation temperature factor [-]. |
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k e |
modified factor of stress concentration [-]. |
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k f |
factor of miscellaneous effects [-]. |
1. Basic endurance limit σ' e
If you do not have available results of material tests of the selected weld joint material and do not know the exact value of basic endurance limit, you can estimate its value. The calculation designs the basic endurance limit using the following empirical formulas:
σ' e ≈ 0.5 S U - for reversed bending
σ' e ≈ 0.4 S U - for reversed traction - pressure
σ' e ≈ 0.28 S U - for reversed torsion (shear)
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S u |
ultimate tensile strength [MPa, psi] |
2. Surface factor k a
To describe the dependence of endurance limit on the surface quality, the fatigue strength of fatigue loaded part increases with the increasing surface quality. This effect is more distinctive for the high quality materials. Use experimental curves to describe the effect of surface quality on the endurance limit according to material strength and for variously machined surface.
The following curve for standard quality weld joints is used for the ka factor determination.
3. Size factor k b
The joint size has no effect on the fatigue strength at weld joints loaded with reversed traction - pressure. Therefore, the size factor for this type of loading is k b = 1.
When the joint is loaded with reversed bending or torsion (shear), the joint size can substantially affect its fatigue strength. The strength reduces when joint dimensions increase.
Determination of exact relation of weld size to the joint fatigue strength can only be done by intricate experimental fatigue tests of the specified weld joint. It is practically impossible. Therefore, a simplified theoretic procedure was worked out. The procedure originates from experimental fatigue tests made at smooth test bars of different diameters. This procedure estimates the approximate size of k b factor according to the theory that the corresponding virtual comparative diameter of test bar can be assigned for the particular weld section.
The following are the calculation formulas for the k b factor determination.
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- English units |
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- metric units |
while the following must be followed:
k b ≥ 0.6
k b = 1 for
where a formula is used for calculation of virtual comparative diameter:
4. Reliability factor k c
This factor expresses the influence of required joint reliability in operation to the value of fatigue strength. The factor value is in the<0.5 ... 1> range and the factor is reduced when a requirement for reliability grows. The k c = 1 value corresponds with the 50percent reliability, that is the 50 percent probability of failure of a weld joint loaded with specified fatigue loading.
In common mechanical praxis, the 95 percent reliability of mechanical parts is usual. If a joint failure can threaten human lives or cause substantial financial losses, the weld joint must be designed for greater reliability.
5. Operating temperature factor k d
The effect of operation temperature on the endurance limit substantially depends on the properties of used material. Commonly used structural steels working in the approximate range of -20 to 200°C do not have the endurance limit much dependent on the temperature and the k d = 1 factor can be used.
Design that considers fatigue failure at high temperatures is a complex problem, because generally the interactions of creep, fatigue and metallurgical instabilities occur. Theoretic information describing this problem are not complete and sufficient. Use the results of experimental tests for good determination of k d factor.
6. Modified factor of stress concentration k e
High local stress concentrations originate in a joint when the weld joint is fatigue loaded because of weld notch effect. These concentrations considerably reduce the joint fatigue strength. Modified factor of stress concentration is determined from the k e = 1/K formula, where the fatigue-strength reduction factor K depends on the weld type, shape, design, weld quality, and the weld joint loading. The following are the recommended values of stress concentration factor for the selected weld types and weld loadings.
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Weld type, method of loading |
K |
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Butt end weld loaded with bend and traction - pressure |
1.2 |
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Butt end weld loaded with torsion (shear) |
1.8 |
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T-joint with double-sided butt weld |
2.0 |
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Fillet weld with loading perpendicular |
1.5 |
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Fillet weld with loading parallel to the weld axis |
2.7 |
When considering the arousal of local stress concentrations, the most hazardous parts of weld joint are transitions between the weld and the basic material. For this reason, take care to use a suitable weld design and perfect machining of transition faces if the weld joints are fatigue loaded. Badly welded root of butt weld or unwedded gap in the root of fillet weld have unfavorable influence on the weld fatigue life. Consider the quality of weld design when setting a factor of stress concentration size.
7. Factor of miscellaneous effects k f
All other effects that can reduce or increase the fatigue strength of weld joint (the influence of corrosion, for example) are included in this factor.