Dr. Zhu:

In terms of their potency, for a crack of a given length, a surface crack is at least twice as dangerous as an internal crack (Remember the Griffith equation for the ideal fracture strength where the crack length a is the total length of an edge crack and half the length of an internal crack. Also, for an infinite sheet in far-field tension, for example, the stress intensity for an edge crack is 1.12 times larger than that for an equivalent sub-surface crack which is twice as long). Because of this, fatigue cracks invariably initiate at the surface. If for some reason there are no surface cracks or they are suppressed, fatigue cracks will be driven to initiate in the interior of the sample. For the reasons described above, for a given sized crack, the stress intensity at the tip of a sub-surface crack will be more than half that for an equivalent-sized surface crack; moreover, as it extends below the surface it will be essentially growing in a vacuum and thus be free from the corrosion-assisted fatigue which may occur for the growth of cracks at the surface. Accordingly, for an equivalent distribution of flaw sizes in a sample, the fatigue life where the crack initiates sub-surface will be far in excess of that where the cracks initiate at the surface.

The question that then arises is how to dramatically extend the fatigue lifetime by causing initiation to occur below the surface, as there are data that clearly show the duality of fatigue strengths for surface and sub-surface initiation of cracks. The best way to do this is of course to put the surface in compression which is achieved industrially by techniques as shot-peening, laser shock peening, cold rolling or burnishing, case hardening, nitriding, induction hardening, etc. Many of these surface treatments also induce a work-hardening layer at the surface, which is significantly more stable at higher temperatures where the residual compressive stresses can relax out. Both the surface residual compression and the work-hardened surface layer can be extremely effective in suppressing surface crack initiation and forcing fatigue cracks to initiate sub-surface (such sub-surface cracks are often known as "fish eyes"), with the result that major increases in the fatigue life of the structure or component can be achieved.

ROR

Dr. Zhu:

In terms of their potency, for a crack of a given length, a surface crack is at least twice as dangerous as an internal crack (Remember the Griffith equation for the ideal fracture strength where the crack length a is the total length of an edge crack and half the length of an internal crack. Also, for an infinite sheet in far-field tension, for example, the stress intensity for an edge crack is 1.12 times larger than that for an equivalent sub-surface crack which is twice as long). Because of this, fatigue cracks invariably initiate at the surface. If for some reason there are no surface cracks or they are suppressed, fatigue cracks will be driven to initiate in the interior of the sample. For the reasons described above, for a given sized crack, the stress intensity at the tip of a sub-surface crack will be more than half that for an equivalent-sized surface crack; moreover, as it extends below the surface it will be essentially growing in a vacuum and thus be free from the corrosion-assisted fatigue which may occur for the growth of cracks at the surface. Accordingly, for an equivalent distribution of flaw sizes in a sample, the fatigue life where the crack initiates sub-surface will be far in excess of that where the cracks initiate at the surface.

The question that then arises is how to dramatically extend the fatigue lifetime by causing initiation to occur below the surface, as there are data that clearly show the duality of fatigue strengths for surface and sub-surface initiation of cracks. The best way to do this is of course to put the surface in compression which is achieved industrially by techniques as shot-peening, laser shock peening, cold rolling or burnishing, case hardening, nitriding, induction hardening, etc. Many of these surface treatments also induce a work-hardening layer at the surface, which is significantly more stable at higher temperatures where the residual compressive stresses can relax out. Both the surface residual compression and the work-hardened surface layer can be extremely effective in suppressing surface crack initiation and forcing fatigue cracks to initiate sub-surface (such sub-surface cracks are often known as "fish eyes"), with the result that major increases in the fatigue life of the structure or component can be achieved.

ROR

Robert O Ritchie

Gang Zhu

Dear Professor Robert O Ritchie,

As always, great answer with deep and comprehensive knowledge about the fatigue we read, learn, and enjoy! You have been always inspiring for us!

However, about this question, you have mentioned two crack states, when a crack initiates at the surface and initiates from the sub-surface location, followed by discussing how we can purposefully move the initiation site from the surface to the sub-surface and improve the fatigue performance through it. But I think we should discuss why fatigue crack initiation site transition from the surface to the interior occurs as the stress/strain amplitude dramatically decreases (applying very high-cycle fatigue (VHCF)), as Gang Zhu has mentioned in the description of the question. So, let's see it in another facet!

Based on available models for fatigue crack initiation (suggested by Professor Hael Mughrabi), the major difference between LCF and VHCF regimes in terms of crack initiation is directly related to dislocation behavior. During LCF, due to the high level of stress, the dislocation movement quickly turns from reversible to irreversible, and it gives rise to the creation of a number of Persistent Slip Bands (PSBs) in microstructure close to the surface. These PSBs would be responsible for the initiation of cracks at the surface. In contrast, when stress levels are very low, the dislocation movement can remain reversible until a higher number of cycles in comparison to LCF. However, since cyclic slip almost never remains completely reversible, some surface roughening will develop in final cycles (approximately after 3/4 Nf). It can demonstrate the slow evolution of slip bands in the course of VHCF. Therefore, We can see the presence of surface roughness in both LCF and VHCF. But, it is worth mentioning in the case of VHCF that, either surface roughness is not powerful enough to initiate a surface crack or some interior microstructural damages have led to crack initiation. In other words, by retarding or suppressing the PSB formation, microstructure damaging has adequate time to be the source of cracks interior the sample. This microstructure-based-damaging can be related to the development of triaxial stresses within the microstructure, stress concentration at interface/interphase and subsequent void formation, shearing-induced micro-void formation, the coalescence of small cracks, etc.

These assertions are in compliance with what proposed in the references and what I have personally observed in our researches.

Best regards,

Amirsalar

I guess you are interested on the reason why the nucleation mode changes between high-cycle fatigue to ultra-high cycle fatigue. I think the best answer is that the mechanisms are different in both domains, this is indicated by the different slopes in a Basquin plot of the S-N curve. In the UHCF range the role of inner stress raisers become much more important for nucleation compared with the normal intrusion-extrusion mechanism active at higher stress-amplitudes.

Dear Respected Professors, I would appreciate your all valuable answers and suggestions.

Personally, I also think dislocation reactions, grain boundaries, and irreversibility will play a dominant role in fatigue crack initiation in VHCF or UHCF when surface intrusion, extrusion can not be formed due to low strain level as well explained by Dr.Seyed Amirsalar Anousheh.

"Pan, X., Qian, G., Wu, S. et al. Internal crack characteristics in very-high-cycle fatigue of a gradient structured titanium alloy. Sci Rep 10, 4742 (2020). https://doi.org/10.1038/s41598-020-61484-3 "

As can be reported in the above-mentioned article, an internal big rough area (RA) is found as a crack initiation region in VHCF and it shows a big cleavage facet of 3 times the average grain size.

It also suggests that by the transition of crack initiation mode from specimen surface to the interior, VHCF performance may not be improved. I think fatigue life will be affected by the different crack propagation mode as well.

I hope it may help to understand the mechanism of crack initiation in VHCF, UHCF.

If something is incorrect, I am very thankful for your correction.

Sincerely,

Dear Prof ROR,

The beautiful answer for the fundamental question posed by Dr Zhu is impressive and inspiration to the industrialist to improve the fatigue life by changing the crack initiation location in the components under fatigue loading by imposing the compressive stresses and work hardening over the surface. The alternate explanation by Dr Amilsalar and supported by Dr Thao P Bui of dislocation theory.

I would like to bring into your attention of the unified approach developed by Dr K Sadananda and Dr A K Vasudevan, states that the internal stresses and their gradients which are developed in the material under fatigue loading could be the responsible for the change in the crack initiation from surface (in LCF,) to interior (in the case of HCF/VHCF/GCF).

If you look at the modified Kitagawa-Takahasi diagram indicates that the smaller the defect higher the stress required. Based on this, above the endurance limit (in VHCF regime) the crack nucleation require higher stresses which are attained by building the internal stress from dislocation, intrusions and extrusion etc in fatigue loading. These internal stresses may get relax relatively at surface when compared to interior, thus the crack nucleation may initiate at interior rather than surface. This will be further aided by the state of stress and entrapped hydrogen gas environment.

Nani Babu