3 Point Bend Test Problem

[RobertJames]

Hello Everyone,

I am very much a new user of Abaqus and hence I am very sorry if this question seems a bit stupid. I have been trying to model a 3 point bend test of epoxy resin (which should fail due to brittle fracture). Essentially my goal is to evaluate the amount of force required to cause failure in the member. So far I have been able to construct a model using cylinders for the supports and the point of force application (this was done to simulate the three point bend test at the university for later comparison). I believe that all my constraints are correct. However, I am not completely sure about the properties I should be applying and also what load would be best in this situation.

Currently my success has been limited to seeing deformation to the member but not fracture, this does not match what I know should be happening and despite doing a lot of searching I can't seem to find where I have gone wrong. Again, I am very sorry if this is a stupid question. Any input would be greatly appreciated.

Kind regards

 

[IceBreakerSours]

I suspect you are new to FEA and, if that is true, and I do not mean to scare you, you should know that modeling fracture is non-trivial. It can be done but, assuming you are a beginner, it will take a significant amount of background knowledge of fracture and skill with FEM over a sustained period of time. If you have a lot of support from colleagues etc. who have modeled fracture before, even then it may take a while to accomplish this.

What would be far more reasonable to accomplish is first performing the elastic and, then, the plastic analyses.

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[RobertJames]

Thanks so much for the prompt response! Yes you would be correct, I am quite new to FEA. It sounds like this problem may be significantly more complex than I was first led to believe.

Would you have any suggestions if I was purely concerned with finding the amount of force required to cause failure in a 3 point bend test, is this a more obtainable goal or is this still quite complex? I am very eager to learn how to do this but am struggling to locate the resources to do so. Again, thank you for the reply.

 

[IceBreakerSours]

A clear case of poor management. I would warn my supervisors, if I were you.

Your question raises some higher level questions: What is it that you are trying to do? What are the goals of the project? What sort of experimental data do you have available? What sort of resources are available to you?

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[RobertJames]

At this stage I would say I am trying to recreate a three point bend test in the software. My goal would be to find/calculate the amount of force required to cause complete failure of the specimen, this value is then going to be used to compare existing experimental data from an identical setup using an Instron 3 point bend test. Experimental data shouldn't be a problem (I hope) and resources at this point are limited to what I can find online.

Do you think this can be done? What sort of time frame will I be looking at to achieve this?

 

[IceBreakerSours]

I assume, by "complete failure" you mean to suggest splitting of the specimen into two/multiple pieces. If that is accurate, then it is not going to happen any time soon (> 1 year or more!) - if you have no FE experts around you to support you. By the way, you might want to have a serious conversation with your supervisor about their expectations, goals of the project, etc.. Perhaps, if 'failure' is defined in less restrictive manner (e.g., plastic deformation = 'failure'?), then that will make it a relatively feasible project for you at this stage. But if this is a Masters/PhD thesis, then you may have enough time to learn about fracture theory and modeling, and execute this project successfully.

At first, I think you should simply try to model the elastic deformation - not even plasticity - in a static analysis (using Abaqus/Standard), verify it against analytical/experimental data, play around with it to gain confidence, etc.. Then, after a few weeks perhaps, you might want to incorporate plasticity. To have a model you are confident about with just elastic-plastic material could take more than a month for you.

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[RobertJames]

Yes, you would be right by assuming that - I was hoping to model a full thickness fracture. Thanks again for your input, I appreciate you being honest towards the difficultly of this problem. Just out of interest, what exactly makes the modelling of fracture such a long and time consuming process?

I guess at the moment I will have to discuss with my supervisor and reach a more achievable definition of failure in this case. I have experimented quite a bit over the past two weeks in regards to elastic and plastic deformation and have come reasonably confident in this area. What additional information is required to model fractures in Abaqus?

 

[IceBreakerSours]

Have a look at the table of contents in these links and see if any of the keywords make any sense (and then I will answer your question):

http://civil.colorado.edu/~saouma/Lecture-Notes/lecfrac.pdf

By the way, you should opinions from others as well. Talk to a fracture mechanics engineer/faculty/student to get a broader perspective.

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[RobertJames]

Very sorry, I may have been a bit misleading when I mentioned I was a beginner. I have very limited knowledge in regard to FEA modelling, however, I am much more familiar in regards to fracture mechanics and the actual theory behind what I am trying to do. This also applies to my resources - very sorry, I originally thought you were purely referring to Abaqus resources. I suppose my problem is not so much understanding what is happening in this case, but rather how I can properly construct a model. Sorry for the confusion.

 

[IceBreakerSours]

Okay, if you are good with the theory of fracture mechanics (linear elastic or above), then getting a handle on modeling fracture using FEM should not be terribly hard. It will probably take a few months of sustained effort. Your best resource will be Abaqus documentation; start with the Interactive Edition and CAE User's Guide and then Analysis User's Guide, and finally, Theory Guide (if you wish to become an expert). Not everything in each of those books will be relevant to your work so you will have to use common sense to pick and choose relevant chapters.

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[mrgoldthorpe]

Robert,

For the model you'll need at the very least the elastic modulus and Poisson's ratio of the epoxy. If the test shows significant non-linear behaviour prior to fracture you'll also need the plastic behaviour in terms of say (yield) stress versus equivalent plastic strain. Do you have such data for the epoxy?

Now that model will only simulate the elastic or elastic-plastic behaviour of your 3PB specimen. So you can obtain output such as load, load-line displacement, crack mouth opening displacement and stress intensity factor or J-integral. You could make comparisons between load, CMOD and K (J) at the test fracture load with your FE results.

However, the model won't "fracture" because there is no implicit constitutive behaviour within your FE model that will cause the model to "break".

If you haven't yet done the actual tests but are doing the FE to make some estimates of failure load, perhaps you could do a literature search to find typical values of fracture toughness for your epoxy (as well as the tensile properties noted in my para 1).

Having said that, there are standard K-calibrations for test specimens so, given values of E and Poisson's ratio, you could do that without FEA.

I agree with IBS that you need to talk to your supervisor about the goals of the FE modelling.

 

[RobertJames]

Thank you both for your replies, they have been very helpful and informative. Mrholdthorpe, at this stage I have managed to create a model that implements both elastic and plastic behavior. The experimental tests have already been completed, the hope of this model was to duplicate the results that were produced. If I was to only consider the elastic and plastic behavior of the model, would you have any suggests in regards to reproducing a situation that would behave similarly to the experimental setup. Again, I am quite new to Abaqus and am not very familiar with all of its capabilities. I am hoping to learn this gradually, but any help would be greatly appreciated.

I have also spent some time reading through the Abaqus documentation that was suggested and have come across the section on fracture mechanics. It seems to suggest that fracture can be modeled using either seam cracks or contour integrals. Should I be investigating along these lines if I am wanting to model fracture in my bend test model? What would you suggest as a next step once I am comfortable creating elastic and plastic models?

 

[adfergusson]

You've mentioned plastic behavior, but does your epoxy exhibit any signs of bulk plastic deformation? Does your load vs displacement graph from your tests show evidence of plastic deformation? Also/alternatively, if there was bulk plastic deformation then you would see this on the fracture surface as a white and/or textured region. If the fracture surface is the same colour as the bulk material and is smooth then failure was brittle (ignoring crack tip plasticity) so incorporating plasticity in your bulk material model would be inconsistent with reality.

If your goal is simply to predict when an epoxy beam will fail in flexure then just run the material and model as linear-elastic and look for the displacement that gives you a peak tensile strain in the material that is equal to the tensile strain of your epoxy... of course you could just do this by hand (and/or use excel, matlab, python/scipy/numpy, etc...) but I guess that wouldn't provide the pretty pictures your supervisor wants from FEA? Or is there some reason I'm missing that warrants the use of ABAQUS for this?

If you want to model fracture then you will need fracture toughness properties (these vary drastically between epoxies, resins we blend and test for use as composite matrices exhibit differences in fracture energy on the order of thousands of percent) unless you are using a very well researched system (in which case take values from academic literature, but with a pinch of salt). Once you have that data you can then start looking at modelling fracture. If you are starting this work as part of a PhD then have a look into XFEM (there's some capability for implementing it natively within ABAQUS). SSA (ABAQUS reseller; I don't work for them but we do purchase our licensees through them) have tutorials on how to use ABAQUS's shiny GUI to implement XFEM which would start you off on the practical side of using XFEM: Link Before delving into such an approach it might be worth looking into issues arising from using a method that is based on numerically solving the weak form of systems of PDEs in a non-conservative manner (i.e. conventional finite element method) vs those that can solve PDEs in a conservative manner (e.g. finite/control volume method).... assuming you can find a co-supervisor who has a clue about FEA/numerical methods, or you back yourself to figure it out on your own.