Abstract
Simulations from a numerical implementation of the phase-field model for brittle fracture are compared against analytical and experimental results in order to explore the verification and validation of the method. It is found that while the intrinsic length scale associated with the phase-field model can be set arbitrarily, the scale of the fracture process zone, and the scale at which the elastic field attains the corresponding analytical brittle fracture limit could be substantially larger than this intrinsic length. It is demonstrated that with a suitable choice of this length scale, phase-field simulations can provide valid predictions of the growth of cracks in quasi-static brittle fracture.
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Notes
There was a minor typographical error in the formula for \(K_I (a)\) in Rubinstein (1985).
Curving vs kinking: The crack paths shown in Fig. 17a are all smooth curves; when the crack was far from the hole, mode II loading increases gradually from zero as the crack approaches the vicinity of the hole. In contrast, if the hole was drilled close to the initial crack, the loading generated a finite jump in mode II loading, and hence the crack initiated with a kink relative to the initial crack. Here, we have only analyzed those experiments that involved a smooth curving of the crack.
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Acknowledgements
Parts of this work were performed during the course of an investigation into failure under a related research program funded by the Army Research Office (Grant Number: W911NF-13-1-0220). The computations performed as part of this work were supported by a generous allocation of time by the Texas Advanced Computing Center. The authors gratefully acknowledge this support.
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Pham, K.H., Ravi-Chandar, K. & Landis, C.M. Experimental validation of a phase-field model for fracture. Int J Fract 205, 83–101 (2017). https://doi.org/10.1007/s10704-017-0185-3
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DOI: https://doi.org/10.1007/s10704-017-0185-3