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Drucker Prager plasticity model for ceramics

Hi everybody,

I am a phD student modelling the behaviour of the ceramics under nanoindentation using ABAQUS. I have read that Drucker Prager plasticity model is suitable for ceramics under indentation. To obtain these parameters ABAQUS users manual suggest doing a triaxial test, but I can not find any information relating triaxial test with ceramics (I only find it for soils and rock). Does anybody know another way  to obtain these parameters? Has anybody performed this test experimentally before?




I know that people at Sandia National Labs have done triaxial tests on various types of ceramics. You will probably be able to find information on silicon carbide and tungsten carbide from Rebecca Brannon.  However, such data will be for macroscopic tests.

I'm not sure that triax tests can be done for nanoscale specimens (say 100 nm).  I would be very interested to know how such experiments may be performed.  Could some nanotesting experts on this forum explain?

Perhaps I don't understand the point of the whole exercise of simulating your problem in Abaqus.  I was under the impression that nanoindentation tests are used to determine certain mechanical properties of materials at the nanoscale.   Such tests are needed because some mechanical behaviors are dramatically different at the nanoscale from what they are at the macroscale.   If that is true then you goal should be to first generate a material model for ceramics at the nanoscale using nanoindentation and other tests.  Once you have the model you can then try to simulate it using ANSYS.    If you don't have experiments at hand then you should try to simulate the ceramic from atomistics up and use those results to fit a nanoscale Druger-Prager (or any other model) and then use ANSYS to check your model.

Can you explain what I'm failing to understand in your plan?

-- Biswajit 


Hi Biswajit,

Thanks a lot for your help. You are right, once I have the properties from experiments I am going to simulate the nanoindentation in FE. Initially my idea is to perform the triaxial test in the macroscale and see if I can obtain the parameters for Drucker-Prager model, but as you pointed out, these properties may differ a lot from the nanoscale. One remarkable difference is the plasticity behaviour. Once I know there have been some experiments with ceramics in the macroscale, the next thing I can do is finding out how I am going to correlate these values into the nanoscale or find if somebody has done it before in the nanoscale. I ignore the later one.

Does anybody know about this? 




You will have to be a bit careful in applying the Drucker-Prager criterion at the nanoscale. The Drucker-Prager criterion is a version of J2 plasticity that includes I1 (pressure) dependence.  In macroscopic samples of ceramics/rocks that pressure dependence comes primarily from compression/collapse of pores.  These pores range in size from a micron to several hundred microns.  I'm not sure whether pores of smaller size have much effect on the I1 dependence of the yield stress because the grains are usually larger than 1 micron.

Also note that dislocations don't play much role in the plastic behavior of most ceramics.  I would guess that there should be very little pressure dependence of the plastic behavior of ceramic materials at the nanoscale.  I don't think much work has been done on pressure dependence at small length scales and many of the mechanisms involved are not well understood.  Good luck on your research.

-- Biswajit 

Hi, Biswajit

If you think the Drucker-Prager criterion as a failure surface instead of a yield surface, is it possible that the growth of small cracks (flaws) are depending on the pressure state?

For instance, the ceramics is much more easy to break at tensile stress, although at the same level of the second stress invariant. Thus, it can be related to the first stress invariant, although I am not sure whether it is appropriate to apply this theory to ceramics...




You are right that the hydrostatic component of the stress close to microcracks plays an important role in determining when certain brittle materials fail.   A group of materials where it is easy to see the effect of microcracks are anthracite coals.  Such coals form under extremely high pressures (and relatively high temperatures) and hence have small porosity.  However, a huge number of minute microcracks form as soon as a tunnel is dug through the coal seam because of the release of the pressure.  So, clearly the growth of small cracks depends on the pressure (even if you never reach hydrostatic tension).

Take a sample of that coal and run it once under uniaxial compression - just enough that the microcracks propagate a bit but not enough to cause failure.  You can actually see feel the cracks if you run your finger over the surface of the specimen.   Now If you take the sample and test it under triaxial compression you'll find that the microcracks close up.  The result is that the stress to failure goes up with increasing pressure.

The Drucker-Prager model is a phenomenological macroscopic model.  The particular mechaism that causes pressure dependence at the microscale can be any of a number of things - whether it is pores or microscracks or something else.  However, that does not matter as long as the desired phenomenon can be reproduced by the model.   My own opinion is that a cross between Mohr-Coulomb and Drucker-Prager with tension and compression caps represents the actual behavior or rock and ceramics better.  An example is Fossum and Brannon's GEOMODEL .

-- Biswajit 

Hi everyone

I,m looking for way to  convert the Mohr-coulomb parameters to Drucker-prager . my Moh-coulomb parameters are:

friction angle = 7.41

Diliation angle=0

Hardening = 791MPa

please help me

So yhanks

my email :

Pandi.Pitchai's picture

I am PhD student at Italy. I would like to apply drucker pragger criterion for ceramic material at micro scale level and to implement this method in abaqus I trying to find plastic properties such as yield stress , internal friction  and cohession from lietrature but unfortunately there is no much information about plastic properties of this materials. I request any knows how to find the plastic properties of cermaic kindly let me know. Also, I need to know how to modify the DP criteriaon for multiaxial loading case.

I am PhD student at iraq. I would like to apply drucker prager Concrete material at micro scale level and to implement this method in abaqus I trying to find plastic properties such as yield stress , internal friction and cohesion from literature but unfortunately there is no much information about plastic properties of this materials. I request any knows how to find the plastic properties of concrete kindly let me know. Also, I need to know how to modify the DP criterion for multiaxial loading case.

What are the values ​​that must be incorporated in the program a model for Ansys Drucker prager for concrete

Hello from me too,

I am also a PhD student, but in the UK. At the moment I am modelling the rolling procedure of a tyre on a deformable surface (soil).

However all the material definitions that I use for my models have been found through the literature review. Thus I am not entirely sure for the respective behaviour that my models exhibit.

Is there any chance any of you might have some accurate Soil Material Properties for sand,mud or any other type of soil. Preferably for the Drucker-Prager (defined as Cap plasticity in Abaqus, took me a while to underastand that :), hope to save some time from any feature students with this note), but Mohr-Coulomb works fine also.

Thank you for any reply and for you time reading this post.

Kindest Regards,



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