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# Anti-fatigue-fracture hydrogels

**Summary** **(Lin et al., Sci. Adv. 2019; 5: eaau8528) : **Designing nano-crystalline domains gives extremely anti-fatigue-fracture hydrogels for artificial cartilages and soft robots.

**Abstract:** The emerging applications of hydrogels in devices and machines require these soft materials to maintain robustness under cyclic mechanical loads. Whereas hydrogels have been made tough to resist fracture under a single cycle of mechanical load, these toughened gels still suffer from fatigue fracture under multiple cycles of loads. The reported fatigue threshold (i.e., the minimal fracture energy at which crack propagation occurs under cyclic loads) for synthetic hydrogels is on the order of 1–100 J/m2, which is primarily associated with the energy required to fracture a single layer of polymer chains per unit area. Here, we demonstrate that the controlled introduction of crystallinity in hydrogels can significantly enhance their fatigue thresholds, since the process of fracturing crystalline domains for fatigue-crack propagation requires much higher energy than fracturing a single layer of polymer chains. The fatigue threshold of polyvinyl alcohol (PVA) with a crystallinity of 18.9 wt.% in the swollen state can exceed 1,000 J/m2. We further develop a strategy to enhance the anti-fatigue-fracture properties of PVA hydrogels, but still maintain their high water contents and low moduli by patterning highly-crystalline regions in the hydrogels. The current work not only reveals an anti-fatigue-fracture mechanism in hydrogels but also provides a practical method to design anti-fatigue-fracture hydrogels for diverse applications.

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## Comments

## Very nice work

Dear Shaoting,

Congratulations on this very nice work. Look forward to more development in the field of fatigue of hydrogels!

Sincerely,

Ruobing

## Hi Ruobing,

Hi Ruobing,

Thanks! Also congratulations on your nice review on fatigue of hydrogels! The set of papers on fatigue-fracture in your group truly inspire people and motivate people to develop anti-fatigue-fracture hydrogels for applications which require long-term robustness.

Best,

Shaoting

## fracture toughness is defined on a sharp crack

Nice work but I find your photos showed a notch, not a sharp tip.

## Hi Roy,

Hi Roy,

Thanks for your comment. In our experiment, a pre-crack was cut using a razor blade with tip radius of around 200 um, simulating the sharp crack tip at undeformed state. The image shown here is at deformed state. I attached the schematic as below showing for the single-notch test specimen with a sharp pre-cut at undeformed state [1].

[1] A. Gent, et al. Cut growth and fatigue of rubbers. I. The relationship between cut growth and fatigue. 8, 455-466 (1964)

## in the figure you report G, but I guess this is really Delta_G

In any case, this is not the same as Delta_K. Obviously G==K^2, so when you make delta_G=Gmax-Gmin this is not the same as delta_K^2. The troubles start when you want to examine the effect of mean values. Have you tried different load ratios R?

## Thanks for the comment. Here,

Thanks for the comment. Here, we applied cyclic loading with Gmax= G and Gmin=0, therefore the G in this figure is delta G as you mentioned. People usually used G instead of K in highly stretchable materials such as elastomers [1-3] and hydrogels [4]. I attached one representative curve of crack extension versus tearing energy for elastomers as below for reference [1]. In this work, we kept Gmin=0 and didn’t vary the load ratio of R=Gmax/Gmin. People did show effect of Gmin in rubbers that exhibit strain-crystallization [5]. It would be interesting to investigate the effect of load ratio on anti-fatigue-fracture properties of nano-crystalline hydrogels in future works. Thanks for the suggestion!

[1] A. Gent, P. Lindley, A. J. J. o. A. P. S. Thomas, Cut growth and fatigue of rubbers. I. The relationship between cut growth and fatigue.

8, 455-466 (1964).[2] G. Lake, P. J. J. o. A. P. S. Lindley, The mechanical fatigue limit for rubber.

9, 1233-1251 (1965).[3] G. Lake, P. J. J. o. A. P. S. Lindley, Cut growth and fatigue of rubbers. II. Experiments on a noncrystallizing rubber.

8, 707-721 (1964).[4] R. Bai, Q. Yang, J. Tang, X. P. Morelle, J. Vlassak, Z. J. E. M. L. Suo, Fatigue fracture of tough hydrogels.

15, 91-96 (2017).[5] W. Mars, A. J. R. C. Fatemi, Technology, Factors that affect the fatigue life of rubber: a literature survey.

77, 391-412 (2004).## you seem to find a rather linear relationship, unlike classical

If I read correctly, your da/dN is rather linear with G. This would be equivalent, in the language of metals crack growth with Paris law, more or less to da/dN=C Kmax^2, which means m=2, the exponential crack growth. This case is an interesting limit case. Among the main consequences of having m=2 are

1) when you integrate the law between initial size a1 and final size a2, normally for m>>2, the effect of final crack size (which gives then influence of static toughness) is very limited. With m=2, the integral is logarithmic, and hence static toughness cannot be neglected

2) if you have a certain distribution of cracks, normally you would expect a distribution of fatigue lives. What we found recently is that the case you are invoquing (m=2 ) leads to extremely reduced scatter. See

[PDF] researchgate.net

On the distribution and scatter of fatigue lives obtained by integration of

crack growthcurves: Does initialcracksize distribution matter?MCiavarella, A Papangelo - Engineering Fracture Mechanics, 2018 - ElsevierBy integrating the simple deterministic Paris' law from a distribution of initial defects, in theform of a Frechet extreme value distribution, it was known that a distribution of Weibull

distribution of fatigue lives follows exactly. However, it had escaped previous researchers …

## Thanks for the insightful

Thanks for the insightful discussion. In this work, we particularly focused on the fatigue threshold (the minimal fracture energy at which crack propagation occurs under cyclic loads).To identify this number from experiment, we linearly extrapolated the curve of d

c/dNvs. G to the intercept with the abscissa, to obtain the critical energy release rate Gc, which gives the fatigue threshold.Regarding the shape of the curve of d

c/dNversus G, the curve shown in this paper was focused on the region with very small value of dc/dN, in which the relation between dc/dNand G approximates linear. However, the overall crack extension curve is truly nonlinear. Particular when dc/dNis moderate high, m is larger than 2. For elastomers, people showed that m =2 when dc/dNis small and m = 4 at moderate dc/dN[1-2].Regarding the interesting case of m=2, I agree with your argument that the integral is logarithmic with m = 2. Also, I enjoy reading your work on effect of distributions of cracks on the distributions of fatigue life.

[1] A. Gent, P. Lindley, A. J. J. o. A. P. S. Thomas, Cut growth and fatigue of rubbers. I. The relationship between cut growth and fatigue.

8, 455-466 (1964).[2] G. Lake, P. J. J. o. A. P. S. Lindley, The mechanical fatigue limit for rubber.

9, 1233-1251 (1965).## you are just 1 order of magnitude below a metal!

Congratulations. I prefer to speak about Kth instead of Gth because it is more common.

For very low cristallinity you find

kth= Sqrt (114 15 10^3) =1.3 kPa m^1/2

to high cristallinity

kth= Sqrt (10 1200 10^6) = Sqrt (12 10^9) = 0.111 MPa m^1/2

so an increase of 2 orders of magnitude, and just one order of magnitude lower than a metal which by comparison would have kth of the order of 1-5 MPa m^1/2 .....

## Thanks!

Thanks!

## notice incidentally that if you define a problem

classically in terms of a remote stress and a crack size, the problem is indifferent on E, and hence the DKth formulation is more interesting. If you reach a value close to a metal in these respects it is even more fascinating.

## Nice work

Hi Shaoting,

Nice to meet you on imechanica. Very beautiful work. The anti-fatigue mechanism for hydrogels is always our concern since we study the topic. You show the crystalline zone strengthening PVA can achieve this goal. The Ashby plot on the final figure well summarized the recent development in this field. I have 2 short questions after reading the paper:

(1) It is known that nature rubber (NR) can also form crystalline zone after stretched, but its fatigue threshold is only 50 J/m2. Have you ever thought about the reason of the big difference on the fatigue threshold between NR and PVA hydrogel?

(2) What is the dc/dN ~ G curve like in the high G zone in Fig. 3F?

Thank you for sharing this great paper with us.

Jingda

Hi Jingda,

Thanks for your insightful discussion. We thought about the difference between nature rubber with strain induced crystallization and PVA hydrogels. The main difference may come from the different types of crystalline domains. The strain-crystallization in natural rubbers is reversible. The crystalline domains mostly dissapear when releasing the natural rubbers to undeformed state, but the cyrstalline domains form and preserve in undeformed as-prepared PVA samples.

If I refer correctly, Lake [1] measured the fatigue threshold of nature rubber in this paper which is 50 J/m2. They particularly focused on the case with cut growth at small deformations. At small deformations, strain-crystallization is only activated in the region at crack tip. The crack may still propagate by cutting amorphus chains instead of fracturing the crystalline domains at crack tip. The paper also mentioned the other effect coming from ozone attacking, which is not the case in swollen PVA in water either.

It would be very interesting to investigate fatigue behaviors in varous semi-crystalline soft materials in future works.

For the dc/dN ～G curve at high G zone, it is truly nolinear with m larger than 2 if we fit the curve into Paris Law as I discussed with Mike.

BTW, your papers on fatigue fracure of hydrogels motivate the study in fatigue fracture in hydrogels. Look forward to more interesting results.

[1] G. Lake, P. J. J. o. A. P. S. Lindley, The mechanical fatigue limit for rubber.

9, 1233-1251 (1965).Shaoting

## Crystallization in NR

Hi Jingda,

Regarding natural rubber, I recall the crystallization melting temperature is below the room temperature. As a result, crystallization forms when the natural rubber undergoes large stretch (e.g., at the crack tip), but melts when the stretch is released. For comparison, the crystallization of PVA is (largely) thermodynamically stable at room temperature.

People have indeed studied crack deflection in fatigue crack growth of natural rubber. See:

[1] 2010 Le Cam The mechanism of fatigue crack growth in rubbers under severe loading: the effect of stress-induced crystallization

[2] 2011 Saintier Cyclic loadings and crystallization of natural rubber: An explanation of fatigue crack propagation reinforcement under a positive loading ratio

If you cut a rubber band with a notch, and cyclically stretch it, you can observe the rough crack surface growing by eye. I'm fascinated to wonder why the threshold of NR is only 50 J/m2. Perhaps it's because the crystallization domain around the crack front is too small, as Shaoting mentioned. However, this "self-activated" composite effect deserves further development in soft materials.

Best,

Ruobing