The Introduction of Shear Modification to Gurson Model

I have been asked questions about how the shear modification was introduced to the Gurson model. I was also asked to compare my modification (see Xue L., Constitutive modeling of void shearing effect in ductile fracture of porous materials, Engineering Fracture Mechanics, 2008, 75(11):3343-3366) to John Hutchinson's modification (Nahshon, K., Hutchinson, J.W., Modification of the Gurson model for shear failure. European Journal of Mechanics A/Solids, 2008, 27:1-17).

I recall when Professor John Hutchinson at Harvard University was invited to join my thesis committee in May 2005 when I was a graduate student at MIT ready to defend my thesis proposal, I was excited that I can have someone who has been working with fracture for many years in my committee, because I have some new exciting development (as least to me) to show. My thesis was on an old topic of mechanics - the ductile fracture modeling, in particular for metals. I developed my macroscopic damage plasticity model (developed August 2004 and coded in February 2005, first submitted to the Journal of the Mechanics and Physics of Solids in February 2005, rejected, second submission to the International Journal of Solids and Structures in May 2005, rejected, third submission to the same journal in July 2005, finally got accepted and published in 2007 and is now among the most cited papers in the same year in IJSS) and a modified Gurson model (developed and coded April 2005 and first presented and published in the EMMC9 proceedings 2006 (Xue L., Void shearing effect in ductile fracture of porous materials, in Local Approach to Fracture, Ed. Besson, J. et al, Proceedings of the 9th European Mechanics of Materials Conference (EMMC9), pp. 483-488, May 9-12, 2006, Moret-sur-Loing, France) and later accepted for publication in a special issue dedicated to EMMC9 '2006 (Xue L., Constitutive modeling of void shearing effect in ductile fracture of porous materials, Engineering Fracture Mechanics, 2008, 75(11):3343-3366, also among the most cited papers published in EFM in the same year).

Similar to my experiences of two rejections of my paper on macroscopic damage model, I was also criticized heavily when I held my first thesis committee meeting in July 2005. Professor Hutchinson was a strong believer that ductile fracture does not depend on the 3rd stress invariant (J3) at that time and was not ready to accept my new models. However, the fight on the subject was well contained. I hold my ground and did not give in by responding with collected and organized experimental results from literature and my own simulation results, which showed many new welcoming features that were not been able to achieve for decades by finite element simulations.  John's opinion pretty much reflected the general consensus of the ductile fracture community at that time, although glimmers of the J3 dependent void evolution already existed (e.g. Zhang K.S., Bai J.B., Francois D., Numerical analysis of the influence of the Lode parameter on void growth, International Journal of Solids and Structures, 2001, 38:5847–5856 and Gao X. and Kim J., Modeling of ductile fracture: Significance of void coalescence, International Journal of Solids and Structures, 2006, 43(20): 627-6293). While it is now widely accepted that ductile fracture of metals is J3 dependent and many phenomena weren't readily explained by the conventional I1-J2 models can be nowadays explained and simulated using numerical tools with the new I1-J2-J3 models.

Fortunately, I was eventually able to convince John and my thesis committee that ductile fracture of metals is J3 dependent and such effect is not trivial with both my damage plasticity model and my modification to Gurson type model. To my surprise, Professor Hutchinson was the first to adopt my modification to the Gurson's model outside my own laboratory led by my advisor Professor Tomasz Wierzbicki. John and his student Ken Nahshon soon published a paper in 2008 that examined the instability condition of my approach to the shear modification of the Gurson-type model. In their examination, they chose a similar J3 dependence function (but no reason was given). Since there are infinitely many such J3 functions as a phenomenological description to give zero at deviatoric tension and compression and to give unity at deviatoric shear condition, such modifications are trivial.

I am glad to see that the shear modifications to Gurson model I introduced in 2005 has been accepted by many research groups worldwide. There are several versions of such shear modification in literature now. Overall, I think they should all predict more or less the same results and are capable of predicting ductile fracture in more details than early versions.