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Viscoelastic cracks: a discrepancy of factor 2.42 found with respect to Wang, Lu, Barber and Thouless and Schapery classical solution

Mike Ciavarella's picture

Wang, Lu, Barber, & Thouless (WLBT, 2016) have written recently an interesting paper on the crack growth in visco-elastic and creeping materials, using a simple Maxwell "liquid" material, and the Double Cantilever Beam (DCB) model under pure moment. Using correspondence principle, they obtained an analytical solution for a viscoelastic beam on an elastic foundation, corresponding to a simple linear force-separation law for the cohesive law. This beam solution gives exact crack growth speed in the limit when the thickness of the beam is very thin, and the stress field is therefore very remote from the singular stress field of classical fracture mechanics. For other situations, WLBT gave FEM solutions, and found "empirically" that a certain dimensionless crack velocity can be expressed as a function of a single non-dimensional group, instead of the two non-dimensional groups predicted by standard dimensional analysis. We show here that this finding is much less surprising considering the Schapery classical solution gives exactly the solution in terms of these single dimensional group, which is the same as that of the beam regime and since the middle regime appears rather limited, this explains the WLBT rather well. The picture is quite clear: for small loads, the universal solution for a semi-infinite crack with a small cohesive zone is recovered. We find however a discrepancy of a factor 2.42 in predicted velocity from the Schapery analysis, which we are not able to explain – but it could be due to numerical convergence in the FEM results.

Since the paper is under review, if anyone can explain this discrepancy factor, you are welcome to be my coauthor!

 

https://www.researchgate.net/publication/350194789_An_analysis_of_the_Wa...

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