Discussion of fracture paper #1 - A contol volume model

This is a premiere: my first contribution to the new ESIS' blog announced in January. Why comment on papers in a scientific journal after they have passed the review process already? Not to question their quality, of course, but animating a vital virtue of science again, namely discussion. The pressure to publish has increased so much that one may doubt whether there is enough time left to read scientific papers. This impression is substantiated by my experience as a referee. Some submitted manuscripts have to be rejected just because they treat a subject, which conclusively has been dealt years before - and the authors just don’t realise. So much to my and Stefano’s intention and motivation to start this project.

Here is my first “object of preference”:

Ehsan Barati, Younes Alizadeh, Jamshid Aghazadeh Mohandesi, "J-integral evaluation of austenitic-martensitic functionally graded steel in plates weakened by U-notches", Engineering Fracture Mechanics, Vol. 77, Issue 16, 2010, pp. 3341-3358.

The comment

It is the concept of a finite “control” or “elementary volume” which puzzles me. It is introduced to establish “a link between the elastic strain energy E(e) and the J-integral” as the authors state. Rice’s integral introduced for homogeneous hyperelastic materials is path-independent and hence does not need anything like a characteristic volume. This is basically its favourable feature qualifying it as a fracture mechanics parameter relating the work done by external forces to the intensity of the near-tip stress and strain fields.

Fig. 2 (a) schematically presents this control volume in a homogeneous material, and the authors find that “the control volume boundary in homogeneous steel is semi-circular”. But how is it determined and what is the gain of it?

Introducing a characteristic volume for homogeneous materials undermines 40 years of fracture mechanics in my eyes..

One might argue that the introduction of this volume is necessary or beneficial for functionally graded materials (FGM). The authors state however that “comparison of the J-integral evaluated by two integration paths has shown that the path-independent property of the J-integral is valid also for FGMs”. Whether or not this is true (there are numerous publications on “correction terms” to be introduced for multi-phase materials), it questions the necessity of introducing a “control volume”. There is another point confusing me. The J-integral is a quantity of continuum mechanics knowing nothing about the microstructure of a material. The austenite and martensite phases of the FGM differ by their ultimate tensile strength and their fracture toughness. Neither of the two material parameters affects the (applied) J, only Young’s modulus does in elasticity. Hence it does not surprise that J emerged as path-independent! The authors compare J-integral values of homogeneous and FG materials for some defined stress level at the notch root in Fig. 10. The differences appear as minor. Should we seriously expect, that a comparison of the critical fracture load predicted by Jcr and the experimental results (Fig. 16) will provide more than a validation of the classical J concept for homogeneous brittle materials?

Not to forget: The authors deserve thanks that they actually present experimental data for a validation of their concept, which positively distinguishes their paper from many others!

W. Brocks