Recently, I've read chapter 12 of "Mechanical metallurgy" which is written by Dieter. When he mentioned SN curve, he said that there is fatigue limit(or endurance limit) in Ti & Steel's curve. I wonder why this phenomenon is only exist in these materials?
For some material like Ti & Steel's curve have well define fatigue life but some other material the fatigue life is a function of number of cycle like aluminum. So we can say here the fatigue strength is depends on no. of cycle i.e. it has different different fatigue strength. So this material has always a finite fatigue life but Steel can have both finite and infinite fatigue life. This is a micro-structural phenomenon of material.
Fatigue failure results from accumulation of fatigue damage. Assuming a perfect electropolished sample without notches, fatigue damage starts by localization of plastic strain which may lead to micro crack initiation within grains (transgranular) or in grain boundaries (intergranular). The growth of the individual micro cracks are impeded by grain boundaries and/or grain junctions. The ability of the micro cracks to pass these obstacles depends e.g. on the stacking fault energy (SFE) of the material. In materials with high SFE the dislocations can easily cross slip and pass obstacles. Same goes for micro cracks. I.e. in materials with high SFE (like pure metals) the micro cracks can easily propagate (an accumulate) to form macro cracks. Eventually this lead to fatigue failure.
If a material has low SFE (like e.g. steel and Titanium alloys) and the imposed load/strain amplitude is low, the micro cracks may not be able to overcome the obstacles (grain boundaries or junctions) and no macro cracks will form. Thus, the accumulated fatigue damage in insufficient to form fatigue failure - i.e. the material will show a break on the SN curve interpreted as a fatigue limit.
It is still being discussed, if a true fatigue limit actually exists. Maybe it's just a matter of imposing enough load cycles to induce sufficient localized plastic strain so that the micro cracks can overcome the obstacles and start propagation to form macro cracks and eventually fatigue failure.
It's due to dislocation pinning by interstitial impurities: C and N in steel, O in Ti. Below a critical stress, the dislocations don't move at all; so no possibility of cyclic strain accumulation and localisation leading to crack initiation. SFE has effects on cross slip and hence cyclic strain accumulation only if the dislocations can move in the first place. AFAIR, the SFE of Ti isn't especially low anyway, Also, I think that SFE will only affect crack propagation by effects on reversibilty of slip in the crack tip plastic zone, rather than acting directly on the cracks in some way as Jesper proposes.
I love the comments by Jesper and Steve and I totally agree with them. But I would like to mention that this is a typical statement which are coming from 'mechanical metallurgy', where all materials are usually assumed as pure and theoretical correct. If you ask the people from 'strength of materials', which are dealing with phenomenological aspects of real material with a lot of imperfections inside, then most of them talking about that the fatigue limit for metallic materials doesn't exist. See latest achievements in gigacycle fatigue and for example look at this two papers [1] and [2].
[1] C. Berger, B. Pyttel, and D. Schwerdt, “Beyond HCF – Is there a fatigue limit?,” Materialwissenschaft und Werkstofftechnik, vol. 39, no. 10, pp. 769–776, Oct. 2008.
[2] Bathias, “There is no infinite fatigue life in metallic materials,” Fatigue & Fracture of Engineering Materials & Structures, vol. 22, no. 7, pp. 559–565, Jul. 1999.
I absolutely agree with Adam's comments: real materials contain lots of imperfections. But this is not the reason why the fatigue limit doesn't exist. The imperfections will impede dislocation movement and some materials require gigacycles (or more) in order to fail by fatigue. I believe that all metallic materials will eventually fail by fatigue when subjected to alternating loads. It's just a matter of imposing enough loads - and that requires time and patience :-)
I also agree with Steve that SFE will affect crack propagation by effects on reversibility of slip in the crack tip plastic zone. And this is what eventually will determine if a micro crack can overcome an obstacle and proceed it's growth.
Many obstacles/imperfections in the material makes it difficult for the micro cracks to initiate and grow. But it only takes one macro crack to make the material fail.
I have answered a question similar to this earlier in RG (the question was on why certain materials show a horizontal portion in their S-N curve while others have a continuously decreasing S-N curve. Tried my best to pull-out that post but somehow could not locate). Repeating the answer once again,
The shape of the S-N curve (particularly if it will have a horizontal part or not) is due to a metallurgical phenomena called "strain ageing" (pl read some basic mechanical metallurgy to understand strain ageing. BTW, the Mechanical Metallurgy by Dieter has a section on strain ageing in chapter 6). In short, strain ageing is a phenomena in which dislocations are pinned down by solute atoms, thereby producing an increase in yield stress (you require higher stresses to unlock these dislocations and cause deformation). Certain materials / alloy systems are strain ageing type while others are not. If you are dealing with strain ageing type of materials (steel, for example as given by Dieter), the strength of the material actually change during cyclic deformation (fatigue). In a way, it is as if you are dealing with a material whose yield stress is now different. It might not matter at high stress amplitudes, since the applied stress levels might be sufficient enough to cause a fatigue failure. By the time you reach the lower stress amplitudes, the stress enhancement in the material due to strain ageing becomes significant. So your applied stress is not enough to cause failure (within a reasonable time). Strain ageing type materials therefore will show a horizontal lower part in the their S-N curve, as if they have an infinite fatigue life (we call it fatigue limit). Materials that cannot strain age (majority of non-ferrous alloys) do not have this advantage. They have one fixed strength level and for every stress amplitude, there will be a definite fatigue life (with a proportional change). Non-strain ageing materials will therefore show a continuously decreasing S-N curve, and for all practical purposes we define a fatigue endurance (life corresponding to 10^8 cycles).
I think that fatigue lime is directly related to the yield point on the cyclic stress-strain curve. Therefore, the materials with a saturated cyclic response, tend to have stabilised stress-strain curve and more-or-less distinct yield point on it, which is close to fatigue limit. Whilst for the materials without stabilised cyclic stress-strain curve, it is not possible to identify the yield point on it, so they don't have a distinct fatigue limit.
Fatigue limits are great for industrial engineering (fatigue thresholds also) as they make an industrial engineers job much easier. They enable engineers to ignore plant made from materials which have a fatigue limit and for which the vast majority of components will never fail during the 10-40years that the plant operates.
Of course any fatigue failures that do occur will be attributed to (i) a surface defect (ii) corrosion (iii) wear scars (iv) too high an alternating loading (v) an overload (vi) wrong heat treatment (vii) the proximity of a weld (viii) a stress concentration...etc..... Never will the existence of a fatigue limit be questioned in general engineering practice.
Of course the scientists are correct, stacking fault energies, dislocation movement, pinning with interstitial solutes, strain hardening, microcrack nucleation and growth. All play an important role in the inherent fatigue limit of a material, if one exists. However, the things that really matter to practical fatigue failures in real plant are (i) to (viii) etc etc etc etc.....
Fatigue of any materials is normally results from the damage accumulation during the fatigue life of that material. Off course the rate of this damage accumulation is govern by the applied stress ratio. Therefore, in some materials there is a fatigue or endurance limit which is simply the stress ratio below which the fatigue failure will not happen. The reason behind this phenomenon is related to the micro-cracking inside the material which in turn is highly related to the applied stress ratio. For concrete and some cementitious materials, for example, if the stress ratio is low i.e., within elastic rang of the materials this will result no damage or permanent deformation in the materials. Thus, there is no fatigue failure. On the other hand, at higher stress ratios the behavior of the materials will be in nonlinear zone. In the latter zone there is a micro-cracking and hence a damage accumulation which will cause the fatigue failure after certain number of cycles .
I think the endurance limit and fatigue limit are not same..all materials do have a fatigue limit if the high cycle fatigue tests at that frequency can be run for 10^8 cycles but this does not ensure the flattening of S-N curve. Flattening of S-N curve which corresponds to Endurance limit does not occur in major non ferrous elements like Al, Mg, Cu but when they are alloyed like 6061 Al alloy (Al-Mg-Si) is having a Endurance limit but not always like 2024 Alloy (Al-Cu-Mg-Si) does not have an endurance limit..it can be a good study what is the effect of gradual copper addition in Al-Mg-Si system on Endurance limit..I have not googled but may be available...where easy glide is favored and slip blocking is not favored in FCC endurance limit does not exist like most FCC metals like Cu, Al and Ni (Experimental Investigation of Crack Initiation in Face-Centered Cubic Materials in the High and Very High Cycle Fatigue Regime by Straub Thomas) but some of them find endurance limit at Gigacycle fatigue regime beyond 10^10 cycles like Ni. Where wavy slip is preferred for BCC (at least for Fe, Nb, Ta you can found in attached link) are found to show distinct endurance limit on a S-N curve. Strain ageing may be a cause for alloying but for pure metals a cottrell atmosphere is absent.
P.S. Good to see Dr. S Sivaprasad and Mike ( M.W.Spindler ) interacting on this topic
Article Influence of loading frequency on high cycle fatigue propert...
Some comments on the strain ageing phenomenon - the name used in the metallurgy area. The mechanism description of this phenomenon given by S. Sivaprasad matches the isotropic hardening phenomena - the name used in the plasticity theory. According to me, it does not explain the existence of the fatigue limit. If you take into account that real material structure is inhomogeneous, you must come to a conclusion that it is only a matter of scale to find a spot in the material where some irreversible changes occur inducing fatigue damage under arbitrary low cyclic loading. Someone could say that those induced damages could be blocked, but ... the material structure was changed, it is unstoppable only the process of damage accumulation rate was slowed down.
Steve Roberts is correct. SFE affects the dislocation structure and only indirectly affects the crack growth. In fact in very Low SFE one can get restricted slip and faceted mode of crack growth. The reason why the endurance limit is not sharp in some alloys is mostly due to their environmental sensitivity. Ti alloys is typical example. There is ultimate endurance as govern by the stress needed for a crack to emit dislocation since fatigue is plasticity induced damage. Someone had a model in defining VHCF limit to dislocation emission from crack tip as derived by Rice and Thomson.
Fatigue limit should exist for all materials. Fatigue is a plasticity induced process. The minimum stress should correspond to the nucleation and propagation of a dislocation from the crack tip. There is no fatigue damage if the material is perfectly elastic. Environment affects both dislocation initiation and propagation - see Hydrogen effects. Sensitivity of bcc and fcc materials to environment can be different. Hope this helps.
I understand this is very old but I am confused by Jasper's answer because steel is BCC. The BCC does not have stacking faults due to the lack of close packed planes.
Kaiju - here is one example - you may be able to find more on Google.
Jobu Awatani, Kazumune Katagiri, Kazuo Koyanagi, A study on the effect of stacking fault energy on fatigue crack propagation as deduced from dislocation patterns, Metallurgical Transactions A, April 1979, Volume 10, pp 503–507|
Stainless steels at low Delta K also should show faceted mode of crack growth. We did some work on Udiment 700 and it also showed faceted mode of crack growth which is reflection of low SFE.
If the applied stress is very low, the deformation will be mainly controlled by primary slip on the active slip systems. Over that if the stacking fault energy is low (e.g. for steels) mostly the slip will be planar with a high degree of reversibility. Moreover, generation of positive and negative dislocations from the same sources on the same slip plane can annihilate each-other and give rise to a localized dynamical equilibrium condition. These factors will create a favorable condition for infinite life, if it exist at all. You can read the Fatigue of Materials by S. Suresh. The fatigue mechanism is explained very well.
It is not that only one mechanism will operate, but as the stress level is usually very low, it is mainly associated the possibility of crack initiation. If the stress level is too low (below CRSS of a single crystal of the material) there may be no plastic deformation at all. Moreover, even if the stress is slightly above the CRSS, the strain aging or dislocation pinning can increase the stress required for further deformation.
Hope this will add to the understanding.
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