What is the difference between them, and how are their influences on the fatigue strength, especially in a notch?
Since this question remains dormant for some time, let me try to address it. My response is based on the book "Mechanical Metallurgy" by G.E. Dieter, and my discussion will not be a complete one.
Residual stress: This is present in a component because of non-equilibrium processing conditions such as welding, rolling, casting, shot peening etc. The maximum magnitude of residual stress will be yield strength of the material. If residual stresses are present, the component will have stress gradient, and stresses of different signs at different locations. For example, shot peening will introduce compressive residual stresses on the surface of a material (say, a few mm deep), and for mechanical equilibrium the core of the component will have tensile residual stress. The residual stress needs to be superimposed on the external stresses for design calculations. The compressive residual stress will decrease the magnitude of external tensile stress - this is how we increase the fatigue resistance by shot peening.
Assembling stress: When bolts and nuts are used for assembling, the bolt will be under tensile stress, and the flange will be under compressive stress. In a weld assembly, the weld metal will be under tensile stress (sometimes it is difficult to differentiate between assembly stress and residual stress), and the adjacent region will be under compression. Bending stresses are expected for shafts when assembled.
Mean stress: In a fluctuating load condition, the mean stress is given by
σmean = (σmax + σmin)/2. Mean stress can also be a steady stress applied to a component such as axial stress of a shaft in a machine.
Fatigue strength: This is denoted as endurance stress, σe, at which no failure is expected to occur even after 20 million cycles or more (some times half billion cycles).
Effect of notch: Notch is going to decrease the fatigue strength by a quantity Kf called as "fatigue stress concentration factor" given by Neuber's relation. This is different from theoretical stress concentration factor, Kt. The theoretical stress concentration factor Kt is geometry related, whereas Kf is a function of several factors including strength of material, and loading type & magnitude.
To answer your question: "how are their influences on the fatigue strength, especially in a notch? " The type of loading and stress level may influence the fatigue stress concentration factor of a notch and reduce the fatigue strength. However, when you look at the Neuber's relation:
Kf = 1+[(Kt-1)/(1+√(ρ’/r))] you will notice that the material constant ( ρ’ ), and radius of root of notch (r), determine the notch effect and not the type of loading!
However, all the stresses are to be considered for the calculation of stress amplitude (σa) to determine the fatigue life using the S-N curve or while using the Goodman relation:
(σa/σe) + (σmean/σuts) = 1
Thank you very much for the kind, accurate, and detailed descriptions and discussions for easily understanding.
I would like to add some other discussions:
(1) The Goodman relation is useful for many engineering problems especially in the case of the smooth specimen. In the notch where has a sharp stress raiser, the mean stress is hard to be treated with, because the sharp stress gradient exists and the elastic region and the plastic region are mixed there. The fatigue notch factor (or fatigue stress concentration factor) is important, and in some cases the Neuber's relation is useful for the analyses.
(2) The residual stress and the assembling stress are different from the mean stress by the definitions. These two stresses are static stress, and relaxations of them by the cyclic loading always occur. In the case of welded joints, the residual stress is created by the deformation of cooling volume shrinkage and phase transformation from high temperature with constraints in the component, and the assembling stress is created by correcting this deformation in the bolt fixation etc. It is considered adequate that the effect of the two stresses is comparable. To reveal the common relation or power law may be an interesting subject.
(3) At the notch where the notch radius is zero, the stress would become infinitely large. The local strain approach would be appropriate for analyses. Because a fatigue fracture is created and propagated in principle by the accumulation of small cyclic strains in a local area, the converted elastic stress or pseudo elastic stress calculated (derived) from the strain values in a certain range would be used for the analyses, in a notch root like the weld toe where the plastic deformation occurs at the local limited area but not in the sample as a whole. The strains can be measured by strain gauges etc. in some cases. The fatigue strength had a linear relationship with the assembling strain (or the assembling converted elastic stress) at the weld toe of test samples in some my studies.
On the other hand, the fracture mechanics approach would also be appropriate for the analyses.
Dear Gyoko Oh
Check the following link,it may help you.
https://www.efatigue.com/training/Chapter_8.pdf
dear Gyoko Oh
maybe these articles can help you.
DOI:10.1007/978-1-4612-4866-8_9
DOI:10.1115/1.4008327
DOI: 10.1083/jcb.102.4.1464
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