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Network imperfection in fatigue of elastomer

Thu, 2019-03-21 16:18

In reply to interesting thoughts

Dear Shengqiang,

I agree with you that, if network imperfection is the dominant factor, the difference between static fatigue threshold and cyclic-fatigue threshold should not be unique to hydrogels, but should be generic for other polymer networks.

For elastomers, both cyclic fatigue (e.g. Lake & Lindley, 1965; Lake & Thomas, 1967) and static fatigue (e.g. Ahagon & Gent, 1975) have been studied. Threshold for cyclic fatigue is about 50 J/m2. Threshold for static fatigue has a range, from ~40 to ~80 J/m2.  It’s hard to say whether the two thresholds are the same or not just by looking at the numbers.  The uncertainty comes from many reasons. For example, natural rubber vulcanizate is used for cyclic fatigue test (Lake & Lindley, 1965), while polybutadiene elastomer is used in static fatigue test (Ahagon & Gent, 1975). The chemistry of polymer network, crosslinking density, synthesize procedure and temperature, etc., are scattering factors to the measurements.  Mechanical performances of elastomers are often viscoelastic.  In static fatigue test, viscoelastic effect can be minimized by using low loading speed.  By contrast, in cyclic fatigue test, the loading speed is usually fast because of practical reason.  Viscoelasticity can relax during the repeated loading and unloading. But to what extent can we ignore viscoelasticity? Crack growth shouldn’t happen only after fully viscoelastic relaxation.  To get rid of viscoelasticity, tests can be done under elevated temperature or using oil swollen elastomers.  But I haven’t seen any literature exclusively studying static fatigue and cyclic fatigue in elastomers.  Network imperfection has been intensively studied in elastomers. But its role in fatigue is blank.

For hydrogels, the beauty is that a hydrogel of high water content is highly stretchable but negligibly viscous. We can disregard viscoelasticity in most cases. Poroelasticity shows up in hydrogels but in a controllable and predictable way. Experiments on the compare of static fatigue and cyclic fatigue are very limited. Available data are contributed by Jingda Tang (J. Tang, et. al, 2017).  The experiments were not on purpose carried out to study the difference between static fatigue and cyclic fatigue. But their data do show that the static fatigue threshold (somewhere between 14.7 and 19.3 J/m2) is larger than the cyclic fatigue threshold (somewhere between 7.18 and 4.19 J/m2).   

With existing data, we can’t tell what causes the difference, even we exclude all other factors such as viscoelasticity, chain pull-out or stress corrosion are negligible except poroelasticity and network imperfection. Let’s focus on polyacrylamide hydrogels, based on Jingda’s data, the delay time for fracture ranges from tens of seconds to ~200 seconds, about three orders of magnitude lower than the poroelastic relaxation time given the relevant sample size of 3 mm and D~10^-10 m2/s.  If we surmise network imperfection, we use a material specific length, Gamma/Wf, instead of the sample size.  Here Gamma is the threshold toughness measured in static fatigue and has a unit of J/m2. Wf is the work of fracture (area under stress-stretch curve) measured in tensile test with sufficiently low loading speed and has a unit of J/m3. In the paper, Gamma is on the order of 10 J/m2, Wf has not been reported, but we assume it has the same order of magnitude with that measured under normal speed, on the order of 10^5 J/m3, then these value give a length on the order of 10^-4 m. This is the size of swelling zone/fracture process zone in front of the crack tip. The time needed for poroelastic relaxation of this zone is on the order of 100 s, comparable to experimental data.  These seem to indicate that, on one hand, due to network imperfection, the relevant length is not the sample size, but the material specific length, Gamma/Wf. On the other hand, due to poroelastic relaxation of the swelling zone/fracture process zone, crack propagates and eventually ruptures the hydrogel.  However, the above discussions are based on two assumptions: the value of Wf and the value of Gamma/Wf. Experimental evidences are missing.




interesting thoughts

Thu, 2019-03-21 03:44

In reply to discrepancy between static-fatigue and cyclic-fatigue thresholds

Dear Canhui, 

It is an interesting thought. I look forward to reading the paper. The hypothesis does make sense to me. 

One question: if it is the case, such difference between static fatigue and cyclic-fatigue should not be unique to hydrogel, but can be also seen in dry elastomer, right? Has any one reported that?


Thank you Ruobing. I will

Wed, 2019-03-20 21:59

In reply to Structuring and toughening in nature

Thank you Ruobing. I will carefully read the reference papers. The bio-inspired toughening of soft materials is really an exciting field.

Structuring and toughening in nature

Wed, 2019-03-20 14:00

In reply to Journal Club for March 2019: Fatigue of hydrogels

Dear Tongqing,

1. Here is a beautiful review on the toughening of bones written by Launey, Buehler, and Ritchie [1], together with a recent broader review on toughening bioinspired materials by Wegst, Ritchie, et. al [2]. The fiber-like osteons in a bone have a size on the order of 100 micrometers. The fiber-like cell-wall layers in a bamboo have a similar size. The fibrils composing these structures scale down to ~nm. Crack deflection and twist observed in bones takes place at a scale of 100 micrometers. However, it is probably improper for us to call them single slice of material, since these biological systems really utilize their hierarchical structures for toughening. In addition to crack deflection, energy dissipation through breaking weak bonds between fibers can have a significant contribution. Our current system does not have such a high fidelity. 

2. For building anisotropy in a network, mechanical prestretch is a cheap and effective way. People have also tried microfluidics/shear flow. For certain molecules, such as liquid crystal polymers, in addition to these methods, one can use surface alignment (for thin samples), or alignment induced by external fields such as optical, electric, and magnetic, and then crosslink the network. A recent paper published in Science by the group of Prof. Jian Ping Gong utilizes both mechanical prestretch and regrowth/heal of chemical bonds to achieve anisotropy.

3. Related to the first question, the natural materials really have multiple mechanisms for toughening at multiple scales. This is to some extent similar to the idea of toughening fiber-reinforced composites, where the interfacial bonding is tuned to be intermediate to achieve highest toughness. Also see this related iMechanical Journal Club by Prof. Teng Li: Rethink Wood.

I am personally really excited about this field of bio-inspired structuring and toughening, especially the connection to hydrogels and other soft materials. Many things can be done by learning from nature and combining some creativity.

Best regards,



[1] Launey, M. E., Buehler, M. J., & Ritchie, R. O. (2010). On the mechanistic origins of toughness in bone. Annual review of materials research, 40, 25-53.

[2] Wegst, U. G., Bai, H., Saiz, E., Tomsia, A. P., & Ritchie, R. O. (2015). Bioinspired structural materials. Nature materials, 14(1), 23.

Dear Ruobing,

Wed, 2019-03-20 04:54

In reply to Journal Club for March 2019: Fatigue of hydrogels

Dear Ruobing,

I just read your paper of flaw-insensitive hydrogel. The idea of crack deflection is beautiful. A few questions:

1. When the crack deflects, the remaining part is safe and only one slice of material fails. In nature, such as bones, what is the size of the single slice of material? Could you give some examples?

2. You mentioned you made the anisotropic composite at the molecule level. As I understand, the main anisotropy is introduced by a mechnical prestretch when the material is in use. Is it possible to bulid in the pre-stretch in the molecule level? I heard of IPN before but don't really know how to do it.

3. What if the crack happens to align with the weak direction? I mean what's the solution in nature?

Thank you.


thanks for your interest in the paper

Wed, 2019-03-20 03:27

In reply to Paris' exponent m<2 and behaviour of short cracks

dear Per

 thanks for your interest in our paper.  We simply play some simple statistics using a pure form of Paris' "law", and remark that the case m=2 is "singular" --- with many "damage tolerant" materials (metals, mostly) being in close to that range.  For very high m, like in ceramics, there is wide scatter of static strength, but it makes little sense to use damage tolerant design.  

Short cracks have been studied for long time but they do not follow Paris law, and indeed are not sensitive even to Irwin stress intensity factors.  You can classify them depending on their size with respect to other characteristic sizes in the material, the simplest one being the "Topper-El Haddad" constant a0.   In the end, despite large efforts in the 1980's, there is no engineering treatment for short cracks, and they propagate possibly much faster than Paris' law, making it difficult to design for fatigue using a purely propagation approach, as it is well known.   We point out that "damage tolerant" approach circumvents this problem, by assuming there are large cracks in critical spots of structures, so that Paris' law type of approach may be used -- some people suggest this may be too conservative, but here we are.

Anyway, your story about people being reluctant to accept a theory which predicts non-zero probability of failure even under no load is interesting, and reminds me that somebody told me "damage tolerant" design at one point became not very well accepted by insurance companies which are reluctant to accept there can be "cracks" in a structure.  I don't know the end of that story, but for sure the situation is even worse. Even if we design with damage tolerant, the material constants have statistical distributions (like Paris C and m, as we discuss in the paper), so you can never rule out that there is a small chance even the most conservative of the damage tolerant design may lead to 1 failure every million cases or so.   People say that design proceeds today exactly leading to very high safety margin, but this requires knowing the tails of the distributions of loads, material properties, etc. with fine details.   So although it is possible to enunciate this as a goal, I don't beleive this can be done in reality.  What happens is that there are also several independent tests and one hopes they are sufficient to indicate a problem.   But new lessons always emerge with new solutions, like in the case of 737-Max regarding electronic systems in this case.

Thanks again for your interest.


Dear Canhui

Mon, 2019-03-18 23:39

In reply to discrepancy between static-fatigue and cyclic-fatigue thresholds

Dear Canhui,

Thank you for contributing to this question and providing this understanding. I guess the idea of imperfection echoes Shaoting's statistical model to some extent. It will be very interesting to see how large the contribution of network imperfection can make to the toughness of hydrogels measured in different loading conditions. I look forward to reading your paper.



discrepancy between static-fatigue and cyclic-fatigue thresholds

Mon, 2019-03-18 18:39

In reply to Dear Rong

Dear Ruobing,


Here is one hypothesis we have trying to understand the discrepancy between static-fatigue threshold and cyclic-fatigue threshold of polyacrylamide hydrogel.  In one of our recently submitted papers, we attribute this discrepancy to the network imperfection.  By network imperfection I mean that long chains and short chains coexist in the polymer network.  Subject to a stretch, the short chains will break and the long chains remain intact. The breaking of short chains happens over a large volume of the testing sample. Such distributed chain scission dissipates energy. Unlike poroelastic process and viscoelastic process, distributed chain scission is insensitive to loading rate.   In this sense, the short chains act like solid-like tougheners.  As a result, the distributed chain scission amplifies the threshold for crack growth under a static load, but contributes negligibly to the threshold for crack growth under cyclic load.   In studying the mechanical properties of hydrogels, network imperfection deserves our attention, just as viscoelasticity, and poroelasticity.




Dear Xuanhe

Fri, 2019-03-15 00:56

In reply to Journal Club for March 2019: Fatigue of hydrogels

Dear Xuanhe,

Thank you for your high encouragement and important questions. Indeed, in this preliminary demonstration, although the crack is diverted, it still propagates following the diverted direction when the load is large enough. Therefore, in the paper, we reserved to call the current proposed hydrogel "fatigue-resistance", but rather just flaw-insensitive (not to mention that we did not eliminate fatigue damage in this case). Because the crack is diverted and never propagates along its initial direction until the whole sample ultimately fractures somewhere else, the fatigue threshold is not defined or measured in the experiments. However, we did measure the "degree" of anisotropy necessary to be achieved in terms of the fracture energy ratio between the transverse and aligned directions of the material (Fig. 3 of the paper). Before reaching this anisotropy degree, the crack either propagates along the original direction, or follows some branched or serpentine directions.

In practical applications, if the material is mainly subject to a uniaxial stretch, then this crack deflection strategy can be readily applied, just as the case of living hinges and wrapping straps using fatigue-resistant isotactic polypropylene in our daily life. If the working condition is more complex, one may be able to use the above-mentioned method of tuning the degree of anisotropy to achieve some specific direction of crack propagation. In a linear elastic material, such on-demand direction of crack deflection can be theoretically predicted. One can also make efforts to theoretically predict this in the more complicated hydrogel systems. 

However, I do not think the above way of tuning the degree of anisotropy and achieving on-demand crack deflection is the ultimate solution, and this is related to the third question. Looking at the literature and the great nature, we see that the idea of crack deflection is not new in composites or other materials, from synthesized polypropylene/polyethylene, to fiber-reinforced composites, to many biological systems such as bones and bamboos. Some biological systems can do even better, such as the hierarchical structures of some fish scales and nacres. To push this principle in hydrogels further, the next thing I think worthwhile to pursue, and would like to pursue myself, is to build such a hierarchical structure mechanically finely designed, which can arrest crack with high energy dissipation in all directions. A preliminary idea is to design some laminated/interweaved hydrogel structures, with aligning in all directions. Strong adhesion can be achieved (thanks to a lot of recent works from your group and other colleagues) between different layers or interweaved fibers and matrix to reinforce the whole structure, while the high-energy phase of the aligned polymers/fibers/crystalline domains in different directions can effectively arrest cracks in an isotropic manner. 

I hope I have answered your questions through sharing these perspectives. As you see, I believe the ultimate strategy for resistance to fatigue fracture is to induce some much higher energy dissipation at the crack tip beyond the Lake-Thomas picture. Based on this, I think utilizing hydrogel composites, or some composite effect in hydrogels (such as aligned polymer chains, phase separation like crystallization, etc.) is a promising direction for fatigue-resistant hydrogels. Composites may further benefit the goal of multi-functionality in many hydrogel devices. We can learn a lot from the previous works on other materials of our forerunners, we can learn perhaps even more from nature, and we can potentially create something new.

Best regards,


Fatigue resistance?

Thu, 2019-03-14 22:50

In reply to Journal Club for March 2019: Fatigue of hydrogels

Dear Ruobing,

I studied this beatiful review on "fatigue of hydrogels" right after it was published online, and my group has began to cited it in our recent papers. This J-Club further attracted my attention to your new paper on fatigue resistance in hydrogels [25]. It seems that the fatigue-resistance strategy in [25] is to divert the fatigue crack to different directions. This is a neat idea, but it seems the fatigue crack still propagates in the sample (right?). A few questions:

1. How do you measure (or define) the fatigue threshold in the experiments?

2. How to control such diverted crack propagation in practical applications such as  Stretchable Ionics?

3. Based on (and beyond) the Lake-Thomas model, we proposed a design principle for anti-fatigue-fracture hydrogels is "to make the fatigue crack encounter and fracture objects requiring energies per unit area much higher than that for fracturing a single layer of amorphous polymer chains"[26].  We demonstrated one example that uses nanocrystalline domains to arrest fatigue cracks in hydrogels, achieving fatigue threshold of 1000J/m2 [26]. Would it be possible to design the high-energy phase in [25] to surround and arrest the fatigue crack?



Download and Install MPI from Microsoft

Tue, 2019-03-12 05:44

In reply to Linking Abaqus 6.14-1 with Microsoft Visual Studio 12.0 (2013) and Composer XE 2013 SP1 (Update 1)

I came into the same problem months ago. This message informs you that your comupter lacks the newest edition of MPI, you just need to download and install  msmpisdk.msi  and msmpisetup.exe from Microsoft. Technically all versions of VS and IVF after 2010 can link with abaqus 6.14.

Re: Stretchable materials of high toughness and low hysteresis

Sun, 2019-03-10 18:48

In reply to Journal Club for March 2019: Fatigue of hydrogels

Dear Zhengjin,

Thank you for sharing this work. It will be exciting to see this design principle to be applied in endurant hydrogels in the near future.

Best regards,


Stretchable materials of high toughness and low hysteresis

Sat, 2019-03-09 21:47

In reply to Journal Club for March 2019: Fatigue of hydrogels

Hi Ruobing, 

Thank you for your comprehensive review on this nascent but fast moving field, and your introduction on our recent work on designing endurant stretchable materials. Stretchable materials such as elastomers and gels enable the field of soft (and possibly biocompatible) systems. Examples include stretchable electronics, soft robots, ionotronics, drug delivery, and tissue regeneration. Most applications require stretchable materials that dissipate little energy during normal operation of cyclic loads (low hysteresis), but dissipate much energy to resist rupture (high toughness), and survive prolonged cyclic loads (fatigue resistant). However, from study of you and some other researchers, the current toughening strategy of adding sacrificial bonds(no matter recoverable or not) into the primary network does not help to enhance the endurance of hydrogels under cyclic load. Clearly, existing stretchable materials cannot meet these requirements simultaneously. It is our opportunity to bridge the gap between existing materials and the requirements of real engineering applications.

In our recent work titled "Stretchable materials of high toughness and low hysteresis", we describe a principle of stretchable materials that achieve both high toughness and low hysteresis. We illustrate this principle using a composite of two constituents: a matrix of low elastic modulus, and fibers of high elastic modulus (Fig. 10a in your review). Both the fibers and matrix are stretchable and elastic(low hysteresis). At a crack front, the soft matrix shears greatly, spreading large stretch in a long segment of each fiber. The crack may bifurcate near the fiber/matrix interface and further increase the length of the highly stretched segment. When a fiber ruptures, all the elastic energy stored in the highly stretched segment is released. This process is analogous to that in a single polymer network, but achieves high toughness because rupture releases energy in a fiber segment, rather than that in a polymer chain. The former has a much larger volume than the latter. The composite retains the low hysteresis, but is much tougher and more fatigue-resistant than the constituents.

A composite of uniaxial fibers resists fracture in one direction, but ruptures readily in other directions.  A laminate with multidirectional fibers resists fracture in many directions, but can still delaminate easily. A composite of a three-dimensional lattice of one material in a matrix of a much softer material will resist cracks in all directions. 

The same principle applies to elastomers, gels, and elastomer-gel hybrids. This class of materials provides opportunities to create high-cycle and low-dissipation soft robots and soft human-machine interfaces. 


Fri, 2019-03-08 05:36

In reply to hello i am working in user subroutine abd i get this error please any recommendation to solve it



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Dear Ruobing,

Wed, 2019-03-06 21:01

In reply to Journal Club for March 2019: Fatigue of hydrogels

Dear Ruobing,

Thanks for your explanations on the Lake-Thomas threshold. I now see the point that the poroelasticity always plays a role in affecting the cyclic threshold. 

Your idea of large time-independent elastic-plastic dissipation is important and I understand more clearly now. 

Our data indeed correlates with different crosslink densities. But as you said, there is discrepancy resulting from experimental conditions so that the fitting pre-factor is not quite close to 1.



Re: Pioneer work on fatigue-fracture hydrogels

Wed, 2019-03-06 20:46

In reply to Pioneer work on fatigue-fracture hydrogels

Shaoting:  Thank you for your kind comments.  The development of hydrogels is motivating a large number of people to work on the mechanical behavior of materials.  We no longer have to work on well established commercial materials.  We can cook up new materials, or mix old materials in new ways, or discover properties unimagined before, or just imagine new ways of using hydrogels.  It is an exciting time.  Everyone has an opportunity to do something extraordinary.  Your work has caught international attention, even before you have your PhD.

Pioneer work on fatigue-fracture hydrogels

Wed, 2019-03-06 19:25

In reply to Re: rubber VS hydrogel in fatigue

Dear Zhigang,

It's very nice to see you in the APS meeting. Your talk is as always fascinating. I did learn a lot.

This review and the set of papers on fatigue fracture in hydrogels from your group are the pioneer work for the direction of design of high performance hydrogels for practical applications. One of the merits that excits us is that a new property (i.e., fatigue threshold) is defined for hydrogels. Fatigue threshold is not new for elastomers, which I learned from your fracture mechanics course. But for hydrogels, it is overlooked although the development of tough hydrogels has been for decades.

After I carefully read Jingda and ruobing's papers (have some sense on the mechanisms of fatigue in hydrogels) years ago, I have a strong motivation to improve this property in hydrogels. Xuanhe had a very good sense and told me to find some way to impinge crack over cycles could be way to go. Therefore, I dig into PVA, a well-known hydrogel material developed by Peppas, which can readily form crystalline domains by a few approaches. My recent work (S. Lin, et al, Science Advances, 5, eaau8528, 2019) is still quite preliminary result or little effort toward the target of enhancing this number (fatigue threshold). Biological tissues can smartly assemble to hierachical structures with ordered crystalline domains. However, it turns to be still quite hard to engineer crystalline domains in synthetic hydrogles. I am aware of a few approaches such as cold-drawing, hot-drawing, pre-stretching in air. But these approaches still sacrifice a few other properties such as high water content and superior compliance. BTW, I did notice your group also have a few approaches to enhance fatigue threshold. Look forward to the coming papers in your group and I am eager to read them and learn from them!

Another merit inspired by the pioneer work from your group is that the huge practical implications enabled by the understanding of fatigue fracutre in hydrogels. Hydrogel devices/electronics/robotics are booming in recent years. But most of these work are still limited in laboratory work and far away from practical usages. One of the reasons for the practical limitations of hydrogels for long term usage is their poor fatigue property. Hydrogels can be as strong as wood, can be as tough as rubber, but still easily lose their functions over cyclic usages. Not only due to mechanical fatigue, long term failures or disfunctionalities can also be caused by aging, degradation, etc. Our current collaborative work on ingestible device (X. Liu, et al, Nature Communications, 10, 493, 2019) is an initial trial to demosntrate that ingestible device made of hydrogels can sustain up to one month in a pig stomach. I have the feeling that more and more hydrogel-based devices/electronics/robotics can be eventually practical, thank to the initial foundation work by your group.

I am personally very excited, motivated about and inspired by the hydrogel work from your group, starting from the classical coupled diffusion theory for hydrogels to the recent fracture, fatigue, and adhesion work. It's quite pity that I didn't find chances to talk more with you during this APS meeting since I only stay half day in the meeting conference. Look forward to meeting you and having discussion with you next time, also look forward to your comments and suggestsions.



Dear Tongqing

Wed, 2019-03-06 14:35

In reply to Journal Club for March 2019: Fatigue of hydrogels

Dear Tongqing,

Thank you for the interesting questions.

For many rubbers, my impression from many papers is that the two thresholds coincide, and can be predicted by the Lake-Thomas model. I think this is because the major dissipation in these rubbers is from viscoelasticity, and the viscoelastic relaxation time is very long (> days) so that the frequency of cyclic loads doesn't matter much. I am not aware of any study on time-independent dissipation toughening the static-fatigue threshold. If you know, I'd love to hear. 

For hydrogels, things can be complex. Hydrogels have water, so poroelasticity exists. If a hydrogel dissipates mainly through poroelasticity and viscoelasticity, then I believe indeed the Lake-Thomas model can describe both thresholds. However, the static load can reach equilibrium given enough time, but the cyclic load may never reach equilibrium, but rather a steady state. Even though the dissipation from poroelasticity and viscoelasticity in both cases is small, the local swelling ratio of the network may be different, and the two thresholds may not coincide, despite that they are both predicted by the Lake-Thomas model using different swelling ratios. This corresponds to my answer to Rong. However, for polyacrylamide, such difference seems small.

If a hydrogel has large time-independent elastic-plastic dissipation, then the cyclic- and the static-thresholds can be different by orders of magnitude, as our recent JMPS paper shows.

The Lake-Thomas model is an ideal picture. A discrepancy may result from experimental conditions, or the local swelling ratio that we have not taken care of, or our adaption of the model to hydrogels (for example Fig. 7 does not match well for some water content, but this could result from the assumption of Gaussian chain). In many cases we do find quantitative agreement. If you have additional data to support, I am excited to see them. I am especially interested in some comparison with respect to different crosslink densities.

For the last question, as people pointed out above, peeling has some unique advantage for hydrogels that cannot fully recover their shapes after elongation. In their original paper (1958 Thomas Rupture of rubber. V.), Thomas used different testing methods to measure the cyclic fatigue growth and found some coincidence. Comparison of thresholds using different testing results has not been systematically conducted in hydrogels. Besides, in peeling, different wetting conditions at the crack tip may play an important role, and further link to valid theoretical analysis.

Best regards,


Dear Ruobing,

Wed, 2019-03-06 03:07

In reply to Journal Club for March 2019: Fatigue of hydrogels

Dear Ruobing,

Thanks for such a clear and insightful review. I really learn a lot and I like many new ideas in the review. I have a few questions or comments.

1. Similar to the question of Rong, I wonder what caused the difference of static fatigure threshold, the cyclic fatigue threshold and the Lake-Thomas threshold. Let's say if we can design an experiment such that the time-depenent effects of poroelasticy and viscoelasticy are small, would you think these thresholds coincide?


2. I notice that  you mentioned a few times that the Lake Thomas model could only "qualitatively" predict the threshold. In fact, we have some unpublished data which, to some extent, quantitatively agree with the theoretical prediction. These data may further enrich the available database of "fatigue of hydrogels".


3. A student here in XJTU was trying to conduct the fatigue experiment by peeling test.   Besides the effects you have discussed in your review, such as large/small scale inelasticity, etc, what else benifit do you think we have from a systemtic experiment? Would you comment on that? Thank you!



Dear Ruobing,

Tue, 2019-03-05 18:10

In reply to Dear Rong

Dear Ruobing,

Thanks for the detailed answer. I understand it now. Yes, it would be intersting to study how various toughening mechanisms affects the threshold. It might offer some insights on how the toughening mechanisms affects the molecular structure at crack tip.

Thanks again for the insightful review. Really interesting!




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