Confusion in understanding Hydrostatic Stress context to failure

Hi Mike,

I can try to clarify the questions

1. Yes, hydrostatic stress effect on yielding it is related with the material structure. For porous materials, hydrostatic stress can cause yielding. Imaging a material with voids inside, when it is applied hydrostatic stress, the atomic layers can be dislocated at some level from the void free surface, and these dislocations would represent the plastic yielding (irreversible deformation). For materials without voids, hydrostatic stress only contribute to the volume change, it can not cause the atomic layers misfitting. Thus it does not have influence on the yielding. I have not seen much debate on this to my best knowledge. 

2. The superpostion works as long as the loading is in linear elastic regime

3. Tri-axial loading in experiments might be hard at the current conditions. If you have references about it please feel free to let me know.

Hope this helps.

Kejie

HS stress has no effect on yielding only in the linear deformation limit. When finite rotation effect is taken into account, it may participate the critical yielding event and following process as well, for instance, through kinking and kink banding.

Hi,

All my comments below are applied to metals.

I know that in metals, the hydrostatic part of the stress has no influence on yielding (plastic deformation), and only the deviatoric part of the stress controls the plastic deformation (assuming plastic deformation doesn’t change the volume). This can be verified mathematically using crystal plasticity constitutive equation (see the kinematical relation b/w the shear rate and the plastic velocity gradient and the Schmidt law).  I think this can be also verified through the normality rule (Drucker’s postulate). You can refer to the excellent class notes from Prof. A. Rollett at Carnegie Mellon University: http://neon.mems.cmu.edu/rollett/27750/27750.html.

Just for further discussion, in elastic deformation, the relation between the pressure and the volumetric strain (strain that produces change in volume) is given by the bulk modulus (in case of isotropic material), or by some components of the 4th rank elasticity tensor (in case of anisotropic materials, e.g. for cubic (C11+2C12)/3). I don’t know if the above relations still apply in case of elastic-plastic deformation. Can someone comment on this please?

2. I m not sure if I understand your question correctly, but you can always decompose the stress into hydrostatic part and deviatoric part. The applied uniaxial loading on the specimen (Sigma11) contains a hydrostatic part (p=Sigma11/3) and a deviatoric part (Sigma11-p).

 Thanks,Hamad

A pressure sensitive plasticity model is developed by Drucker and Prager, 1952(DP model). HS is sensitive in this model because the difference between compressive and tensile strength. In this model(not for porous material), The mean stress appears in the yielding function in linear term which is regarded as the displacement of yielding surface.  

For porous material, the influence of hydrostatic pressure to yielding is significant even when the tensile and compressive yield strength is identical. In this model the mean stress appears in the yielding function in quadratic term, which is regarded as shape changing of yielding surface.

The previous two conditions might exist in same material.

No standard experiment method is available as far as I know, but  followed two papers may provide you some useful information concerning HS experiments.

Deshpande, V.S., Fleck, N.A., 1999. Isotropic constitutive models for metallic foams. J. Mech. Phys. Solids, 48, 1253-1283.

Miller, R.E., 2000. A continuum plasticity model of the constitutive and indentation behaviour of foamed metals. Int. J. Mech. Sci. 42, 729-754

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