Dear Masoud,

I can give some information about FCC metals.

One of the first experimental estimation of GND density during low cycle fatigue was given by Mughrabi:

Haël Mughrabi and Bernhard Obst (2005). Misorientations and geometrically necessary dislocations in deformed copper crystals: A microstructural analysis of X-ray rocking curves. Zeitschrift für Metallkunde: Vol. 96, No. 7, pp. 688-697.

It was concluded that only a few percent of the total dislocation density is GND.

My experimental colleagues at Paul Scherrer Institut, during my PhD work, measured the apparent GND density in a copper single crystal during cyclic fatigue:

Ainara Irastorza-Landa et al 2017 Modelling Simul. Mater. Sci. Eng. 25 055010

Effect of pre-existing immobile dislocations on the evolution of geometrically necessary dislocations during fatigue

concluding that a GND density of the order of 1e13 1/m^2 is reached after 100 cycles.

It is true what you said on the vacancy production and there may be some works where the density of vacancies was measured. However, in FCC a more evident phenomenon that leads to crack initiation is the extrusion produced by persistent slip bands reaching the surface. You can see some experimental images in:

Z.S. Basinski, S.J. Basinski

Fundamental aspects of low amplitude cyclic deformation in face-centred cubic crystals

Progress in Materials Science, Volume 36, 1992, Pages 89-148

and some modelling using discrete dislocation dynamics by Christophe Déprés:

First Steps of Crack Initiation and Propagation in Fatigue of FCC Crystals Studied by Dislocation Dynamics

Conference: ASME 2012 11th Biennial Conference on Engineering Systems Design and Analysis, July 2012

You can find more information about this in Christophe Déprés PhD thesis.

A literature review about this topic is reported at the beginning of my PhD thesis:

https://infoscience.epfl.ch/record/223625

I do not have a precise answer to what is the relationship between the SSD or GND density and the low-cycle fatigue life. This must be complicated. In FCC metals, you should look at the factors that are known to produce persistent slip bands. These are dislocation mobility, multiplication and cross slip. GNDs are known to be a minority of all dislocations, so I would say the increase rate of SSD and the rate at which dislocation structures develop are the factors that shorten the fatigue life.

If you find out something more, I am happy to hear back from you.

Best Regards,

Nicolò

Dear Masoud,

The first point that you should consider is the major fraction of life at low-cycle fatigue regime is dedicated to crack propagation. So, the fatigue crack propagation stage is the most important stage in low-cycle fatigue life. Thus, it seems that the vacancy production due to SSDs annihilation can not influence significantly on fatigue life at low-cycle regime! ( Nicolò Grilli )

Generally, existence of statistically stored dislocations (SSDs) in microstructure leads the increment in fatigue crack growth rate (FCGR), specially at an unstable state. So, the high density of SSDs that is the implication for cyclic loading damage, leads to reduction in fatigue life at low-cycle regime.

On the other hand, considering the nature of GNDs (geometrically necessary dislocations (GNDs) are generated and then accumulated at the interface of the phases with different deformation behavior and/or anywhere in the microstructure that the continuity preservation during deformation is needed), the presence of this feature is representative for different slip behaviors at various microstructure regions and/or phases (in multi-phase structures). Therefore, the high frequency of GNDs due to the difference in plasticity leads to homogeneous strain partitioning. In this situation, a significant stress concentration is generated which this may increase the preferential sites for micro-voids formation, coalescence and fatigue crack initiation (A.S. Anoushe, A. Zarei-Hanzaki, H.R. Abedi, A. Barabi, C. Huang, F. Berto, On the microstructure evolution during isothermal low cycle fatigue of β-annealed Ti-6242S titanium alloy: Internal damage mechanism, substructure development and early globularization, Int. J. Fatigue. 116 (2018) 592–601. doi:10.1016/j.ijfatigue.2018.07.014). Also, preferring the mentioned sites for fatigue crack propagation is frequently reported. So, it seems that the increase in GNDs density may cause the reduction in fatigue life.

In addition, I would like to be convinced by your reasons and speculations of the effect of dislocation substructure (cell or wall) on fatigue life reduction that you have reported at your poster "Microstructural characterization of fatigued stainless steels with different strain-hardening behavior by using EBSD and X-ray diffraction line-profile analysis".

Best regards,

Amirsalar

If you believe (as I do) that the fundamental parameter that controls fatigue life (LFC or HCF) is plastic deformation, then just substitute the question, "What is the role of SSD density and GND density on the resistance to plastic deformation?" As you think about that, remember that fatigue is a "weak link" process, and you must consider local strain and not just bulk measurable deformation. This last distinction is really the basis for the Coffin-Manson relationship being so important in real engineering structures of complex geometries, as opposed to the simple specimen geometries usually tested in the laboratory.

Also, read the comment here by Amirsalar Anoushe about crack propagation. The reason Delta-K works so well for crack propagation was demonstrated by Lankford. He found ["Mechanical Behavior of Materials -IV", 1, (1983) pp. 3-29] that there is a correlation between Delta-K and the local cyclic plastic strain at the tip of a crack. So the whole process is:

So just make one more modification your question and pose it as, "What is the role of SSD density and GND density on the resistance to local plastic deformation at the tip of a cycling crack?"

This, combined with the thoughts here by Nicolò Grilli, could lead one to expect minor effects as the answer to your originally posed question.

Dear Nicolò Grilli,

Thank you for your valuable explanation. I agree with most parts of your thought. In the case of crack initiation sites, the extrusions produced by PSBs reaching the surface play a significant role. So, the mentioned effect of SSD accumulation on dislocation cell walls is related to crack propagation sites. The vacancy production due to SSDs annihilation on the cell walls prepares more potential crack propagation sites, and therefore can affect the LCF life (Li et al. Mater. Charact. 14 (2018) 96). I agree with your idea about the effect of PSB characteristics on the LCF life. As you said the fraction of GNDs are small compared with SSDs. But this small fraction of GNDs likely play a significant role on the crack tip during crack propagation as well as SSDs.

Dear Amirsalar Anousheh ,

Many thanks for your answer. I agree with you in the effect of SSDs on FGCR. As you know, the majority of fatigue crack propagation (in LCF) occurs at presence of strongly correlated dislocations (walls and cells). Since most of the screw dislocations already easily annihilated, it can be said that the mechanism of this effect (SSDs on FGCR) is annihilation of SSDs to vacancies in walls and cells, and thus these vacancies act as some potential crack propagation sites.

About the effect of GNDs in a dual phase material, your discussion seems true, however, when it comes to single phase material, it may not correct.