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Critical Experimental and Theoretical Tests for Failure Criteria
A new section has been added to the website http://www.failurecriteria.com/. This is on critical tests for failure criteria. It summarizes most of the previous entries to the website and provides evaluations of the most salient of the failure criteria by comparing with high quality experimental data.
The evaluations are a two step process. First the physical and mathematical basis of any proposed criterion is assessed. After that, the comparison with critical data is accomplished. The failure criteria are applicable to the onset of dominating, irreversible deformation, whether it be due to the inception of major plastic flow, as a form of failure, or explicit brittle failure itself. Thus it is necessary that the evaluation process span the full range of isotropic materials types going from very ductile to very brittles ones.
Primary attention is given to the long standing Coulomb-Mohr form and the recently developed polynomial invariants method. The deficiencies of the former are quantified as well as the accuracy and advantages of the latter. The explicit data bases used for the evaluations are those of (i) the classical Taylor-Quinney results on very ductile metals, (ii) failure data on a very brittle geological material, and (iii) data on a mid-range case of ductility/brittleness.
Although most of the results are for isotropic materials, some results are for application to fiber composite laminates. The usual method of progressive damage is shown to have considerable deficiencies, while the method of polynomial invariants shows promise. Most of all, quality data are needed for a variety of conditions.
- Richard M. Christensen's blog
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Failure of elastomers
Prof. Christensen writes "Failure criteria are not needed for all materials. For example, elastomers and “soft” biological tissues have no need for failure
criteria, such forms are of no relevance for them."
I fail to understand the reasoning behind the argument that failure criteria a not needed for elastomers. I can think of at least four elastomer-related problems that would benefit from a failure criterion/a fracture theory:
1) The space shuttle disaster was due to the failure of an elastomeric gasket.
2) Rubber O-rings in a range of industrial applications. These O-rings undergo large stretches and twists and failure can often has catastrophic consequences.
3) Elastomeric composites (explosives, e.g.) that depend on the development of cracks (or otherwise) for their functioning.
4) The engine mounts on your car which experience huge torques and can fail catastrophically as they did on my Mazda 323.
On another note:
I have been unable to find an analytical solution for mixed mode edge cracks on nonlinear elastomeric materials undergoing large deformations; my particular interest is on mode III type cracks. Can anyone point me to some papers if they exist? If analytical solutions don't exist, can someone explain why?
Thanks,
-- Biswajit
Re: Failure of elastomers
Dear Biswajit,
These articles might be of help to you:
1) Fracture Analysis of Rubber-Like Materials Using Global and Local Approaches: Initiation and Propagation Direction of a Crack
2) Theoretical and numerical limitations for the simulation of crack propagation in natural rubber components.
3) Crack propagation in rubber-like materials
I could send these papers to you if you have no access to them. Paper 2) is an interesting one. I actually got it from Professor Verron. I think he should be able to recommend you quite a bit other references.
Re: Elastomer failure
Dear Alejandro,
Thank you for the links.
The second paper does mention that "crack propagation in elastomers under multiaxial loading conditions remains an open problem." However, I would like to understand why the problem remains open and what approaches (other than numerical) have been tried and why they have failed. The older papers by Sternberg and Knowles might have some hints.
The variational approach to fracture and the related discussions by Ball seem interesting but parts of it are beyond my understanding. Can anyone explain what the deal is with that approach?
-- Biswajit
Failure Criteria
Dear Biswajit,
Thank you for your comments. I was probably too quick and brief with the rather casual comment that failure criteria are not needed for elastomers and soft biological tissues. Of course all materials will fail when loaded beyond some tolerance level. Predicting or at least circumscribing failure conditions for all materials (whether one calls it failure criteria or something else) is vitally important.
An expanded explanation is that I would not have much confidence in applying the types of three dimensional failure criteria in the website to problems of elastomeric failure (I can elaborate on this if you wish). More likely a special nonlinear fracture criterion would be appropriate. I do recall that I mentioned somewhere in that section that the types of 3-D failure criteria of interest and concern are targeted for glassy polymers but not for rubbery polymers. On a broader scale, many elastomeric failure problems are intimately related to physical aging.
Your examples of elastomeric failure are timely and important. The space shuttle disaster has special meaning for me. I was asked to be on the technical subcommittee for the original investigation. Although I was not in a position to do it at the time, I followed it closely, especially since I had worked with elastomers for quite some years. I recall that in congressional testimony Richard Feynman dipped a piece of rubber into ice water and then demonstrated failure. For the space shuttle type of problem and with the polymer below its glass transition temperature I would have no hesitancy about proceeding as follows. Experimentally determine the uniaxial failure strengths T and C for the reduced temperature glassy polymer. Perform a three dimensional finite element solution for the actual problem Then apply the 3-D stress state to the T and C calibrated failure criterion to determine safety or failure.
Perhaps I should mention that the website concerns only failure criteria for homogenous materials under uniform or nearly uniform stress states. Fracture criteria for stress concentration problems of all types is a completely separate matter. Both failure criteria and fracture criteria areas are independent and complementary disciplines, as needed to treat appropriate problems. Sometimes just the terminology can get a little confusing and misleading.
Please let me know if I can try to answer any other questions about the website, or about this particular problem.
Richard Christensen
Failure criteria
Dear Prof. Christensen,
Thank you for your elaboration.
I have often heard from people who work in the composites industry that fatigue does not occur in polymer composites. Perhaps what they mean is that the processes leading to "metal fatigue" are not observed in polymer composites. Nevertheless their statements can be misleading to the layperson (in a relative sense).
Your articles are likely to be read by a wide range of people and is likely be misinterpreted. A footnote clarifying the relevant statement on your website will go a long way in removing such misunderstandings.
-- Biswajit
Fatigue
Dear Biswajit,
Good question, fatigue can be a problem and experience with metals could be misleading. In general fatigue with composites is less of a problem than with metals, but it still must be considered. As with all generalities however, this could be a good way to get into trouble. It’s always best to forget orthodox thinking and simply work with the explicit data bases of relevance.
A big complication with polymer composites is that creep rupture can be very important, and it becomes difficult to “deconvolve” the creep rupture effects (sometimes called static fatigue) from the cyclic fatigue effects. Maybe I will try to get into this topic in the website sometime. Thanks for the suggestion.
Please let me know if I misunderstood your question and I will respond further. It may take me a day or two since I’m on the road right now.
Richard