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Fracture energy for crack propagation in a 4 points bending notched beam

Mai Lan NGUYEN's picture

Hi everyone,

Anyone can tell me how to determine the fracture energy for crack propagation in a 4 points bending notched beam (mode I)?

In fact, in a 4 points bending, there are different displacements: displacement mesured at the upper supports (u), displacement mesured at the midle of the beam (deflection of the beam, f), crack opening displacement (COD), and others ... Among these first two displacements, it's u which corresponds to the mesured force. However, this one includes also bias effect (punching effect = "effet de poiçonnement" in french). So my question is which one of these two displacements must be used to calculate fracture energy?

p/s: the material in my reseach is asphalt concrete which is a thermo-mechanical material. My reseach consists of crack propagation in a 4 points bending beam in asphalt concrete. Moreover, I'm going to use Abaqus to apply in my reseach using cohesive zone model. I will be very glad to have some advices.

Thanks! 

Comments

Mai Lan NGUYEN's picture

I found that there is a document : RILEM TC-50 FMC, "Dtermination of the fracture energy of mortar and concrete by means of three-point bend tests on notched  beams", Mat. Struct. 18 (1985) 285-290.

Anyone can show me this document, please? 

Hi Mai Lan,

 Try to look at these link if you can find any interesting points inside.

http://www.lrrb.org/PDF/200615.pdf 

or: http://www.lrrb.org/pdf/200423.pdf

 Hope it help

 Hamanh

Mai Lan NGUYEN's picture

Hi Hamanh, thank you very much for your help. I've read this document. However, there is no work on four point bending beam (only three points bending). In fact, in a three points bending fracture test, these two types of displacement (displacement mesured at the upper support and deflection of the beam) is the same. Whereas, in a four point bending fracture test, these two displacements are different. So anyone can help me to show which displacement that's needed to determination of fracture energy in a four points bending fracture test?

Best regards 

phunguyen's picture

Hi Mai Lan,

 It is very nice to know one more Vietnamese from the mechanics field.

You have posted your question quite long ago so I assume that it has been solved.

Concerning your question, in my opinion, just plot the load displacement curve of the loading node. Then the area of this curve = the fracture energy since the work of external load must be equal to the dissipated energy. I think the vertical displacement of the loading node is appropriate for this. But I am not sure.

 BTW, I guess that you are working in France now? Could you email to me at V.P.Nguyen@tudelft.nl for more discussing on mechanics and the like?

 P

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