Abstract
The virtual crack closure technique (VCCT) is widely used for calculating energy release rates along crack fronts and modeling the propagation of cracks in solid materials. Although the VCCT formulation for smooth crack fronts has been sufficiently addressed in the literature, the application of VCCT to a nonsmoothed crack front with sharp corners warrants further investigation. The present study describes an enhanced VCCT to calculate energy release rates and stress intensity factors for cracks with arbitrary shapes in 3D domains discretized on structured grids. The formulations of the enhanced VCCT were developed and implemented into a multiphysics simulation environment capable of simulating crack propagation in the framework of linear elastic fracture mechanics. Comparisons with existing analytical/numerical solutions and other VCCT approaches were performed to verify the enhanced VCCT in terms of SIF calculation along nonsmoothed crack fronts. We then applied the enhanced VCCT to a hydraulically driven penny-shaped fracture problem to further demonstrate its capability to simulate nonsmoothed fracture propagation.
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Data Availability
This is a theoretical work for which no data need to be made available.
Code Availability
All the simulations in the present study were performed using an open-source simulation environment GEOSX which can be obtained at https://github.com/GEOSX/GEOSX.
Abbreviations
- ΔE :
-
Energy released from crack extension
- w :
-
Fracture aperture
- b :
-
Element width
- G :
-
Energy release rate
- K I :
-
Stress intensity factor for Mode I
- R 0 :
-
Equivalent crack radius
- R :
-
Fracture radius
- κ :
-
Dimensionless toughness variable
- μ :
-
Fluid dynamic viscosity
- ν :
-
Poisson’s ratio
- f :
-
Nodal force
- ΔA :
-
Virtually closed area
- L :
-
Element length
- G I :
-
Energy release rate for Mode I
- σ :
-
Tensile stress
- Q :
-
Injection rate
- P :
-
Fracture pressure
- K Ic :
-
Fracture toughness
- E :
-
Young’s modulus
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Acknowledgements
This research was supported by the Exascale Computing Project (ECP), Project Number: 17-SC-20-SC, a collaborative effort of two DOE organizations—the Office of Science and the National Nuclear Security Administration—responsible for the planning and preparation of a capable exascale ecosystem—including software, applications, hardware, advanced system engineering, and early testbed platforms—to support the nation's exascale computing imperative. This work performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344. LLNL release number LLNL-JRNL-815419.
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RRS and HW conceived and implemented the enhanced virtual crack closure techniques algorithm. HW, PF and JPM designed the verification examples and the hydraulic fracturing cases. HW performed all the simulations and wrote the paper. All authors participated in discussing the results and reviewing the manuscript.
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Wu, H., Settgast, R.R., Fu, P. et al. An Enhanced Virtual Crack Closure Technique for Stress Intensity Factor Calculation along Arbitrary Crack Fronts and the Application in Hydraulic Fracturing Simulation. Rock Mech Rock Eng 54, 2943–2957 (2021). https://doi.org/10.1007/s00603-021-02428-9
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DOI: https://doi.org/10.1007/s00603-021-02428-9