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Definition of a new predictor for multiaxial fatigue crack nucleation in rubber

ErwanVerron's picture

From an engineering point of view, prediction of fatigue crack nucleation in automotive rubber parts is an essential prerequisite for the design of new components. We have derived a new predictor for fatigue crack nucleation in rubber. It is motivated by microscopic mechanisms induced by fatigue and developed in the framework of Configurational Mechanics. As the occurrence of macroscopic fatigue cracks is the consequence of the growth of pre-existing microscopic defects, the energy release rate of these flaws need to be quantified. It is shown that this microstructural evolution is governed by the smallest eigenvalue of the configurational (Eshelby) stress tensor. Indeed, this quantity appears to be a relevant multiaxial fatigue predictor under proportional loading conditions. Then, its generalization to non-proportional multiaxial fatigue problems is derived. Results show that the present predictor, which covers the previously published predictors, is capable to unify multiaxial fatigue data.

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Dear Erwan, I read your paper with great interest; You have made an excellent attempt to solve the fatigue problem of a complex material. One question came to my mind was how does your experimental data and predictor plots look if you plot in the form of R ratio versus life cycles for different ranges..sort of a Haigh Diagram.Also, I was wondering if you have a computer program or something, which you used to calculation for life predictor. I will really appreciate a copy of the program.Thanks and Keep up the good work

 Nitesh

ErwanVerron's picture

Dear Nitesh,

I think that your comment concerns the well-known fatigue life improvement observed in rubber fatigue. My Ph.D. student Andri Andriyana and I examined this problem in another paper:

http://dx.doi.org/10.1016/j.ijsolstr.2006.06.046

We have examined this problem for uniaxial tension. It was demonstrated that the association of the configurational predictor with a simple viscoelastic constitutive equation (to reproduce the hysteresis loop of the stress-strain response) leads to the prediction of this improvement. Do not hesitate to send me an email, I will send you the paper.

Concerning the program, it is a small Matlab program that is devoted only to simultaneous uniaxial tension and torsion loading conditions. I can also send it to you but I need to translate commentaries in the program because they are in french ...

Erwan

 

Good morning Mr. Verron,

I am a student working in crack development in filled elastomers. I read some of the papers exposed in your blog which are very interesting. I see that many papers mention the FEM method, others try to use a singularity approch in order to propose a stress-field explanation near a crack tip. But I was wondering : what are the mechanisms that create rupture at the scale of the fillers and the chains. I saw a very interesting article from Le Cam who mentioned the nucleation of cavities induced by ZnO. But if there was no ZnO, should we still have cavities (I suppose that yes). But, my main question concerns the cohesion energy between fillers and the matrix, do you know somebody who works in this point of view. Because what is responsible of the nucleation : it is a decohesion, but it was not proved experimentally i think, what is your opinion about it? do you know other papers about this type of study?

Thank you very much for your help. 

Best regards.

infinity.

 

 

ErwanVerron's picture

Dear infinity,

I will try to answer your questions: the ones in this post and the other ones concerning the Mullins effect.

Concerning the influence of fillers on the fracture of rubbers, it is difficult to say if fillers will act against or help crack propagation. For static fracture, I don't know because I did not study it. For fatigue loading conditions, we performed experiments in NR and we saw that the defects which will initiate the crack can be due to cavitation (in the bulk material), decohesion between matrix and additives (including fillers aggregates) and also rupture of fillers aggregates. Nevertheless, until now we were not able to compare filled and unfilled elastomers. We just showed that the ability to crystallize under strain highly increases the resistance of rubber. Moreover, it was demonstrated by Rault et al. that fillers are nucleation sites for crystallization. So, in this way, it can be considered that fillers increase rubber resistance. But, in filled SBR (which does not crystallize under strain), fatigue cracks propagates catastrophically and we did not see the influence of fillers ...

Concerning the Mullins effect, some authors argue that it is due to fillers (see the bibliography in our papers on the subject: doi:10.1016/S0022-5096(01)00136-3 and doi:10.1016/j.jmps.2003.12.006) . Nevertheless, for modelling this behaviour, two main ways are employed. The first one is the Continuum Damage Approach (see doi:10.1016/j.jmps.2003.12.006), other phenomenological approaches reduce to it. The second approach is microstructurally motivated and was initiated by Bueche in the 60s. We tried to extend it for 3D problems in doi:10.1016/S0022-5096(01)00136-3. Nevertheless, we did not make differences between chain-chain links or chain-filler links. Maybe you can check the papers which cite our work to see if there exist improvements to take into account fillers.

Finally, there are different definition of the Mullins effect. The most common ones are the loss of stiffness observed between the two first loading cycles or the loss of stiffness between the first and the fifth cycles. For further cycles, the loss of stiffness is due to viscoelasticity of the amorphous phase and the 'viscous' hysteresis is mainly due to crystallization.

Finally, it was just some comments on your questions. If you are interested, you can contact me by email and I can send you some papers. Moreover, we can discuss about your ideas, because I'm interested in this type of problems.

Bye, 

 

Erwan Verron

Associate Professor

Institut de Recherche en Génie Civil et Mécanique, UMR CNRS 6183

Ecole Centrale de Nantes, France

 

Dear Mr. Verron, 

thank you very much for responding to my questions. I will read the papers you proposed me. For the moment, I try to well understand the mechanical properties of rubber before doing interpretations on crack development in rubber. I see that what happens near a crack tip (in a mechanical understanding) is complicated by many phenomenas like non-linearity, fluing, heating, ... I am also interested by FEM (I have a student version of ABAQUS, I can draw a sample geometry, but it becomes more difficult to introduce a crack in it and to have force ditribution according to the mesh that has been selected, I have never followed courses about ABAQUS, to expensive) If I have more questions I will not hesitate.

I saw that you mentioned the  ECCMR that will be in PARIS. I would like to go to this conference (if my lab can pay the 400euros that the conference demands for Phd students).

I realize that more I study the physical, chemical characterization of the crack development in rubber, more i think i need a mathematical and mechanical point of view, this is not what i expected at the beginning of my study.

  

 

ErwanVerron's picture

Dear infinity,

It is difficult to have both physical/chemical and mechanical skills. I just have the second one. The keypoint is that you should be able to understand some basics of the "other side" in order to help you to conduct relevant investigations.

Concerning the FEM, I'm not sure that using Abaqus is the good starting point, because it is a very complete (and then complicated) finite element code. Maybe there are simpler softwares for small problems (maybe free). As an example, COMSOL is good and quiet easy to use even for non-linear problems. Just have a look on it.

Bye 

Erwan

 

Dear Mr. Verron,

Thank you for your advises, I will try this software (I have also heard about CAST3M and freefem, but i don't think they are useful for what i try to do) and I'll tell you if it helps me more.

Best regards.

infinity. 

ErwanVerron's picture

Hello,

The paper was accepted for publication in JMPS.

Here is the doi: http://dx.doi.org/10.1016/j.jmps.2007.05.019

Bye 

 

      Erwan

Dear Mr. Verron,

 I read one of the article you published with Mr. Marckmann concerning the comparison of hyperelastic models for rubber-like materials, and I must say that this article is very useful because it well explains all the 20 different models : the phenomelogical models, the one where the function sðW/ðI1 and ðW/ðI2 are calculated, and the models based on the physics consideration (that is to say the physics of polymer chains network and the statistical methos). As it well enumerate the different models, i think it would be good to mention this article and to advise it to any person who need a summary, because modelisation in litterature is like a jungle and we can easily get lost.

 

Regards. 

Infinity. 

 

Good morning Mr. Verron,

 I know that there was a colloquium in Dresden this week about filled rubber but I couldn't go there (I have previewed to go to the next technical meeting of the rubber division). I saw that you assisted to this colloquium and I wondered if the colloquium proposed summaries or proceedings for those who couldn't get there ?

Did you find it interesting ? 

 Best regards.

 Infinity.

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