The best relatioship for fracture toughness and fatigue crack growth is Paris Law.

Thank you, Dr. Kumar. Can you provide more details or some articles about it ?

1.The heat input has direct impact on thoughness of weld metal and HAZ. One area to check.

2. The toughness is related to location of fusion line and precrack. 

3. HAZ is complex and simple value fails to represent fracture toughness of weld.

Hope these help.

There are a review of laws betwen fracture thougness e fatigue crack growth in:

Beden, S. M., Abdullah, S., & Ariffin, A. K. (2009). Review of fatigue crack propagation models for metallic components. European Journal of Scientific Research, 28(3), 364-397.

Fundementally, there is little correlation between the fracture toughness and the rate of fatigue crack propagation as the mechanisms of these fracture modes are entirely different. Indeed, in simple terms, plasticity promotes fatigue yet is a toughening mechanism which can enhance the fracture toughness.  One region where they do correlate though is at high rates of fatigue crack growth.  Here as the Kmax in the fatigue cycle approaches the fracture toughness (or alternatively the limit load), static modes of fracture, such as cleavage or microvoid coalescence, can occur during fatigue crack growth in addition to striation crack growth, such that the Paris exponent in this region becomes inversely proportional to the toughness (see Ritchie & Knott, Acta Metall, 1973).

The general observation is that the higher fracture toughness materials suppose to have lower crack growth resistance. It is to be noted that the either fracture or FCG resistance is governed by the crack growth mechanism. Thus, the following factor to be considered

(1) In fracture test the loading is monotonic

(2) In FCG test is done under cyclic loading

Since, the loading conditions are different the crack growth mechanism cab be different.

For example in FCG crack growth governed by extrinsic and intrinsic crack closure mechanism, which play significant role on the crack tip shielding, thereby lead to lower crack growth. Pl. see M. Nani Babu, B. Shashank Dutt, S. Venugopal, G. Sasikala, , A.K. Bhaduri, T. Jayakumar, Baldev Raj, On the anomalous temperature dependency of fatigue crack growth of SS 316(N) weld, Materials Science and Engineering: A, Volume 527, Issue 20, 25 July 2010, Pages 5122–5129.

These effects are not present in the case fracture test.

In addition there are lot of heterogeneity in the weld and residual stress effects on the crack growth mechanism needs to be considered.

If you come to the relation between FCG and fracture, you can also establish between using simple logic. For example take Paris part in the FCG curve and find the slope of the curve, which is nothing but difference in thresholds and KIC/JIC/CTOD and correlate with FCG rate.

I hope this will help you.

with regards

Nani Babu 

There is not correlation between the fracture toughness and the rate of fatigue crack propagation as the microscopic mechanisms of crack growth and loading types of these fracture modes are entirely different.

Hello Mengyu!

In my opinion the explanation of such results can be following.

The weld metal is heat treated due to welding process. That means the weld has different yield stress end ultimate stress than base metal. Furthermore, heat treatment would change the material in such way that it can become strain unhardenable while the base metal can be strain hardenable. This effect can influence the fracture toughness and crack growth rate in deferent way.

To provide more appropriate answer some additional information is needed.  At least yield stress and ultimate stress of weld and base metal.

The fracture toughness is the capability of the materials to withstand a rupture and is thus linked to a high  final rupture strength and a high elongation at rupture.

Fatigue crack growth rate is related to local plasticity of the materials at the tip of the crack once it is initiated and is variable as the crack length increase (Paris law). Thus, one can link fracture toughness to the last stage of crack growth (final rupture) but not to the whole sequence of crack propagation.

The questioner has raised a general question in terms of his specific circumstances and he has perhaps failed to identify a critical factor by which we might be able to avoid speculation.  There many suggestions in the answers above with which I can agree, for example, Ritchie points out that low fracture toughness can cause higher-than-expected fatigue crack growth at high stress intensities, and Matcha properly points out that the loading factors between fracture toughness determination and fatigue crack growth are different.  There are responses with which I would disagree.  Since I discovered the mechanism of fatigue propagation in a ductile metal, I claim the last word.  One would expect that high fracture toughness would correlate with better fatigue crack growth behavior in a ductile metal such as FCC 316 stainless steel, both properties improved by plasticity and freedom from brittle fracture mechanisms.  Murphy's Law demands that fatigue will make use of any property in the material that degrades its strength, and sometimes even the reverse.  Even 316 might be brittle under liquid metal embrittlement, not relevant here.  However, it may be that Chai's weld metal differs in its fatigue resistance from the parent 316 material because of a change in texture or because the welding process changed the chemistry, or the weld metal contains pores that acts as crack stoppers under the conditions in which he performed his fatigue tests, or for other factors operating in cooperation too numerous to mention.  I suggest that Chai might perform metallography on his two materials to reach his own answer.

Fatigue crack growth rate depends on various parameters such as the cyclic delta K, crack depth, load amplitude, environment etc.

Fracture toughness is the limit for K at which crack depth will lead in to a failure by large crack growth.

After the fatigue crack growth for the period of time and number of cycles intended, fracture toughness is used to check if the final crack depth is stable or nor not, that is, is the final crack depth below the maximum depth permitted that will result in the KI within the Kmax.

In the sense that Reddy has interpreted the question, I agree with Reddy.  Others of us interpreted the question in terms of material properties.  I think that the question was directed in the latter sense.

I accidentally saw this discussion two years later but like to make a comment anyway. I agree with Prof. Rob Ritchie that fracture toughness and fatigue crack growth rate are fundamentally different. This topic is a metallurgical issue as some of you have mentioned and I don't want to get to that. In the academic world many topics are easier to understand when an example is given. Many years ago I had to open a fatigue crack in a copper part for examination of the fracture surface. It was practically impossible and the ligament deforemed but not fractured. However, the part had a flat fatigue crack in it with no gross plastic deformation. This is a case of very high fracture toughness but perhaps a low fatigue crack growth rate. This example clearly support the absence of any relation between fracture toughness and the crack growth rate commented by Prof. Ritchie. I also like to ask Chai to be more careful with his wording. I could not understand what he means by statements such as "indicating the crack resistance is higher" in his fatigue crack growth discussion. With much respect for all of you.

If a material has a high fracture toughness associated with a high work hardening rate coupled with high ductility, then I would expect the crack growth resistance in fatigue to be large. In that sense there is a connection between fracture toughness and fatigue. Steels of very high hardness often have low fracture toughness and low crack growth resistance because high hardness steels are very sensitive to aggressive environmental effects on crack growth.

To try and explain what I am arguing, let me give you all an experimental example: Neumann once reported cracking behavior in a Fe-4%Si binary alloy. Such a metal is inherently brittle under the influence of the silicon content and has low fracture toughness. During his tests, Neumann changed the frequency of cycling by a factor of ten, on a periodic basis, all other factors of the test remaining constant. Microscopic examination of the fracture surfaces revealed that, at the lower of his two frequencies, the fatigue striations on the fracture surface were of the ductile variety demonstrating very high local strains at the crack tip and the plastic blunting mechanism of crack growth. For periods of cycling at the higher frequency, the adjacent striation widths were much greater, indicating a huge increase in crack growth rate. Also the fracture surface showed high flatness and river patterns, indicating increments of brittle fracture, but associated plasticity was sufficient to limit the extent of the brittle fracture per cycle. Fe-Si alloy, being bcc, is highly strain rate sensitive and the frequency change, although not very high to judge from monotonic tests, raised the stress at the crack tip sufficiently high, because of the very high localized strain/strain rate at the very tip, to initiate brittle fracture.

The original questioner raised a very complicated question which produced many answers because of hidden assumptions. I hope I have made myself clear.

You are very clear Prof. Laird. I also agree that Chai question was not clear and complicated. He reached for help to interpret his results which could not be found by the way it was asked. But some people responded that he was comparing apples and oranges; i.e. comparing the base metal with the weld metal with two completely different microstructures. Added to that are the size, how many passes, welding condition and procedure. I remeber back in 1970's researchers on welding metallurgy had a difficulty preparing their specimens. So the best answer to Chai was that there is no relation between fracture toughness and the fatigue crack growth rate (presumably as defined by the slope of Paris Law). If I remember right, Paris law is no more linear when approaching very high delta K values near fracture toughness. If that is correct, then the first step to clear this puzzle is to look at da/dn experimental results and look for the existence of a correlation between fracture tough and the crack growth rate at very high stress intensity ranges, doing best to keep the material the same (such as heat treatable aluminum alloys aged to different conditions. Getting involved with these discussion requires time for people not currently doing research. Therefore, I will leave this discussion for those who are currently active in research. but continue to watch and learn.

This has been a fascinating discussion, particularly with such luminaries as Prof. Campbell Laird weighing in. I hate to strike a discordant note here but I thought the original question by Chai was perfectly clear - is there any fundamental relationship between fracture toughness and fatigue-crack propagation resistance?

In reply, I stand by my original response - in general NO! The growth of fatigue cracks in metals is promoted by plasticity - ceramics barely fatigue - yet, on the other hand, plasticity is the prime source of the intrinsic fracture resistance of metals, i.e., their fracture toughness. And so if anything, fatigue crack propagation resistance and fracture toughness should be (approximately) inversely related. Of course, environmental effects, crack closure, and the like, can intervene and act as confounding variables, but strictly speaking fatigue and monotonic fracture are entirely different modes of failure motivated by entirely different fracture mechanisms.

As I pointed out earlier, the one exception is for fatigue crack growth at high stress intensities where the value of Kmax approaches the critical stress intensity for fracture Kc, or where the net section stresses approach the limit load stress. This causes segments of monotonic fracture, such as cleavage, intergranular cracking or microvoid void coalescence ("static modes"), to occur as additional mechanisms to the cyclic fatigue mechanism, e.g., ductile striation growth, during crack advance, leading to an acceleration in growth rates just prior to outright failure. In brittle metals, this can of course occur at somewhat lower growth rates. Correspondingly, if one plots the the Paris slope, m, of the da/dN vs. deltaK curve, the value of m in this regime tends to be inversely related to Kc, although above a toughness of 50 to 80 MPa/m, the magnitude of m "asymptotes" to a value of ~2 which is independent of toughness, as shown in Fig. 15 of Ritchie & Knott, "Mechanisms of fatigue crack growth in low alloy steel". Acta Metall, 1973).

ROR

It is interesting that when studying the fatigue of Al2O3-ceramics, the slope, m, for the Kt-Kd range of the K-V diagram also turned out to be approximately 2.15 (Kuzmenko, Shevchuk, Borovik, "The effect of Loading Frequency on Polycrystal Aluminum Oxide Fatigue". Strength of Materials, 1984). At the cyclic loading in the Kt-Kd range, the crack propagation rate is almost completely dependent on static mechanisms of fracture.

You may be interested to see the recent paper by Jones et al. on metals: 'Crack Growth: Does Microstructure Play a Role'. Eng. Fracture Mechanics, vol 187, 2018, 190-210. Their answers: 'Yes in Fracture Toughness' - but 'No in Fatigue Crack Growth'. Thus, they conclude that there is no relationship between fracture toughness and fatigue crack propagation. I work on polymer -matrix fibre composites, and I am coming to the same view for CFRPs.

The question is interesting and too complex. The obtained results cannot be applied to all materials. Moreover, not knowing the structural transformations in the material.

I completely agree with the answers of professors Campbell Laird, Robert O Ritchie and Nini Babu Matcha

See paper by Jones et al. in Eng Fracture Mechanics. 187, 2018, 190-210. They show that there is no correleltio for metalsn.

Be careful, the conclusion cited about the effect of microstructure on fatigue crack growth "No in Fatigue Crack Growth" does NOT apply to time dependent fatigue crack growth or the near threshold regime.

In general terms, materials with higher fracture toughness exhibit better fatigue properties (better crack propagation behavior, at least). In several case studies, the fracture surface investigations show that the materials with high fracture toughness have a smaller final fracture region (over-load or final rupture).

Indeed, the fracture toughness is completely related to microstructure of material. In this regard, the colony structure in dual phase titanium alloy consists of fully lamellar shape of alpha phase, exhibits the higher fracture toughness in compare to equiaxed microstructure. In fully lamellar microstructure, the considerable fraction of interfaces and boundaries causes to high resistance of fatigue crack propagation and low FCGR!