FailureCriteria.com

Liang,

   Thank you for the  comments.  First, with regard to reference sources, there certainly are many fine ones.  The two you mention are excellent.  It would indeed be helpful if other people share their views on good sources for materials modeling with respect to failure.  In my website on failure criteria I am not doing a broad literature survey.  That would be far more involved than is possible there.  Rather, I am focusing upon the mechanics basis for a few well grounded failure criteria, applicable to particular materials forms in particular failure scenarios.

   With regard to specific failure mechanisms, there are many possibilities.  Two of the  three mechanisms that you mention are explicitly present in the isotropic model in the website.  I  believe the third one (localization) is also there, but on an implicit basis.  On a small enough scale, there is a competition between different failure mechanisms for surpremecy.  The one that "wins" shows up on the macroscopic scale.  This no  doubt is something of an over-simplification but I hope it at least conveys the motivational framework.  For any specific details I must refer back to the website and through that to the papers behind it.

   I would like to add that the apparent reason why progress on modeling failure criteria may seem so slow compared with other branches of mechanics is because it is so very complex.  But a little perspective on the subject suggests that there has been more progress in modeling failure in the past 30 or 40 years than in the previous  200 or 300 years of mechanics history.  It is up to the members of iMechanica (and a few others) to keep this going.

Richard 

Ajit,

    Thank you very much for opening up this rich source of discussion.  I couldn’t agree more, there is no universal, all encompassing, single theoretical methodology for treating failure in materials.  For me, the first dividing line is between treating failure in an idealization of homogeneous materials under homogeneous stress fields, versus treating failure in an idealization of a homogeneous material in the presence of a specific defect, and necessarily under non-homogeneous stress.  The defect is usually but not necessarily of a size scale larger than the characteristic length dimension implicit in the concept of the homogenization.  Once past this dividing line there  could be many more dividing lines for treating various types of failure conditions.

    Does this mean that  we should give up on seeking generality in our methods and approaches?  I don’t think so, but it should be recognized that there can  be a fine line between seeking legitimate generality and merely stretching it beyond all physical realism.  This is exactly the problem I was up against in trying to develop a failure  criterion which would have the Mises form as a limiting case, but still have the power and versatility to include the very different behaviors involved with polymers and ceramics.  By the way, in going to the range of ceramics, which can  be dominated by brittle  behavior, fracture mechanics still was a  strongly guiding influence to me even though the formal methodology involved is certainly not that of fracture mechanics. If nothing else, this is an example of cross fertilization between fields.

    Now let me get to the discussion of Sih’s strain energy density concept in fracture mechanics.  I need to be careful here  because my website is about failure criteria, not fracture mechanics.  Still, there are some related considerations between the two cases.  Knowing that the Mises criterion is also that of critical distortional energy density, it was attractive for me  to try to find a more general energy based form that would cover the other materials classes besides just that of very ductile metals. In this case of failure criteria, that turned out to not be possible.  The failure criterion that I derived and tested necessarily involves the dilatational stress invariant in linear form, not in an energy like quadratic form.  There was no way to avoid this occurrence and as a result, energy has no significant meaning  in this failure criterion.  I discussed this in the first (1997) paper mentioned in the website.  For this reason and others, I would doubt that strain energy has a special role to play in fracture mechanics or in failure in general.

    Strain energy is a key effect in constitutive equations and variational formulations, but not likely so in failure.  Failure characterization, it seems to me, is a stand alone discipline parallel with constitutive equations, but completely independent of it.  Just as there are many different constitutive forms so too there necessarily are different failure forms for different  classes of behavior.

   I hope this may help.  Needless to say, its all still developing and still wide open.

Richard

Liang,

    Although we are coming at this from very different directions, we are arriving at the same conclusion. Namely that strain energy in its various forms is not suitable as a failure criterion.  Actually, this has been known for a very long time, but it gets rediscovered periodically.

    On the other matter, I distinguished failure criteria from constitutive equations, while you view them jointly as part of the overall constitutive behavior.  I think these differences pertain to the level and nature of the two mechanics idealizations and not to a fundamental, physical divergence.  We all are striving to understand and characterize the load bearing capability of materials over the useful range in which they can be employed.  My characterization is just the convenient  and common idealization of the actual behavior. The obvious example is the case of ductile metals idealized as perfectly elastic behavior up until termination in accordance with the Mises  criterion (or equivalent).  In reality, both elastic deformation and irreversible dislocation flow begin with the very first small increment of load and the dislocation flow accelerates thereafter with increasing load up until ultimate rupture.

    I agree with you that in the next few years there likely will be some convergence to a general and common  understanding on these matters.  It should be an exciting and productive time.  All of us are lucky to be a small part of it.

Richard