nach oben

Rock Mechanics and Rock Engineering

Erschienen in:

23.03.2021 | Original Paper

An Enhanced Virtual Crack Closure Technique for Stress Intensity Factor Calculation along Arbitrary Crack Fronts and the Application in Hydraulic Fracturing Simulation

verfasst von: Hui Wu, Randolph R. Settgast, Pengcheng Fu, Joseph P. Morris

Erschienen in: Rock Mechanics and Rock Engineering | Ausgabe 6/2021

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config

KI-gestützte Suche

Aus

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.

Vorheriger Artikel Numerical Investigation on Hydraulic Fracturing of Extreme Limited Entry Perforating in Plug-and-Perforation Completion of Shale Oil Reservoir in Changqing Oilfield, China

Nächster Artikel Creating Cloud-Fracture Network by Flow-induced Microfracturing in Superhot Geothermal Environments

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Alfano G, Crisfield MA (2001) Finite element interface models for delamination analysis of laminated composites: mechanical and computational issues. Int J Numer Methods Eng 50:1701–1736. https://doi.org/10.1016/j.ijsolstr.2010.12.012CrossRef

Banks-Sills L (2010) Update: application of the finite element method to linear elastic fracture mechanics. Appl Mech Rev 63(2):1–17. https://doi.org/10.1115/1.4000798CrossRef

Chan SK, Tuba IS, Wilson WK (1970) On the finite element method in linear fracture mechanics. Eng Fract Mech 2:1–17. https://doi.org/10.1016/0013-7944(70)90026-3CrossRef

Chen M, Zhang S, Li S, Ma X, Zhang X, Zou Y (2020) An explicit algorithm for modeling planar 3D hydraulic fracture growth based on a super-time-stepping method. Int J Solids Struct 191–192:370–389. https://doi.org/10.1016/j.ijsolstr.2020.01.011CrossRef

Chiu TC, Lin HC (2009) Analysis of stress intensity factors for three-dimensional interface crack problems in electronic packages using the virtual crack closure technique. Int J Fract 156:75–96. https://doi.org/10.1007/s10704-009-9348-1CrossRef

De Roeck G, Wahab MMA (1995) Strain energy release rate formulae for 3D finite element. Eng Fract Mech 50(4):569–580. https://doi.org/10.1016/0013-7944(94)00232-7CrossRef

Detournay E (2004) Propagation regimes of fluid-driven fractures in impermeable rocks. Int J Geomech 4(1):35–45. https://doi.org/10.1061/(ASCE)1532-3641(2004)4:1(35)CrossRef

Economides MJ, Nolte KG (2000) Reservoir stimulation, 3rd edn. John Wiley & Sons, West Sussex, UK

Fawaz SA (1998) Application of the virtual crack closure technique to calculate stress intensity factors for through cracks with an elliptical crack front. Eng Fract Mech 59(3):327–342. https://doi.org/10.1016/S0013-7944(97)00126-4CrossRef

Fu P, Johnson SM, Settgast RR, Carrigan CR (2012) Generalized displacement correlation method for estimating stress intensity factors. Eng Fract Mech 88:90–107. https://doi.org/10.1016/j.engfracmech.2012.04.010CrossRef

Fu P, Johnson SM, Carrigan CR (2013) An explicitly coupled hydro-geomechanical model for simulating hydraulic fracturing in arbitrary discrete fracture networks. Int J Numer Anal Meth Geomech 37:2278–2300. https://doi.org/10.1002/nag.2135CrossRef

Fu P, Settgast RR, Hao Y, Morris JP, Ryerson FJ (2017) The influence of hydraulic fracturing on carbon storage performance. J Geophys Res B: Solid Earth 122:9931–9949. https://doi.org/10.1002/2017JB014942CrossRef

Ghadirdokht A, Heidari-Rarani M (2019) Delamination R-curve behavior of curved composite laminates. Compos B Eng 175:107139. https://doi.org/10.1016/j.compositesb.2019.107139CrossRef

Heidari-Rarani M, Sayedain M (2019) Finite element modeling strategies for 2D and 3D delamination propagation in composite DCB specimens using VCCT, CZM and XFEM approaches. Theor Appl Fract Mech 103:102246. https://doi.org/10.1016/j.tafmec.2019.102246CrossRef

Hellen TK (1975) On the method of virtual crack extensions. Int J Numer Methods Eng 9:187–207. https://doi.org/10.1002/nme.1620090114CrossRef

Helsing J, Jonsson A, Peters G (2001) Evaluation of the mode I stress intensity factor for a square crack in 3D. Eng Fract Mech 68(5):605–612. https://doi.org/10.1016/S0013-7944(00)00115-6CrossRef

Huang J, Fu P, Settgast RR, Morris JP, Ryerson FJ (2018) Evaluating a simple fracturing criterion for a hydraulic fracture crossing stress and stiffness contrasts. Rock Mech Rock Eng 52:1657–1670. https://doi.org/10.1007/s00603-018-1679-7CrossRef

Isida M, Yoshida T, Noguchi H (1991) A rectangular crack in an infinite solid, a semi-infinite solid and a finite-thickness plate subjected to tension. Int J Fract 52:79–90. https://doi.org/10.1007/BF00032371CrossRef

Krueger R (2004) Virtual crack closure technique: history, approach, and applications. Appl Mech Rev 57(2):109–143. https://doi.org/10.1115/1.1595677CrossRef

Leski A (2007) Implementation of the virtual crack closure technique in engineering FE calculations. Finite Elem Anal Des 43(3):261–268. https://doi.org/10.1016/j.finel.2006.10.004CrossRef

Liu PF, Hou SJ, Chu JK, Hu XY, Zhou CL, Liu YL, Zheng JY, Zhao A, Yan L (2011) Finite element analysis of postbuckling and delamination of composite laminates using virtual crack closure technique. Compos Struct 93(6):1549–1560. https://doi.org/10.1016/j.compstruct.2010.12.006CrossRef

Livieri P, Segala F (2010) An analysis of three-dimensional planar embedded cracks subjected to uniform tensile stress. Eng Fract Mech 77(11):1656–1664. https://doi.org/10.1016/j.engfracmech.2010.03.035CrossRef

Marjanović M, Meschke G, Vuksanović D (2016) A finite element model for propagating delamination in laminated composite plates based on the virtual crack closure method. Compos Struct 150:8–19. https://doi.org/10.1016/j.compstruct.2016.04.044CrossRef

Mastrojannis EN, Keer LM, Mura T (1979) Stress intensity factor for a plane crack under normal pressure. Int J Fract 15(3):247–258. https://doi.org/10.1007/BF00033223CrossRef

McClure M, Horne RN (2014) An investigation of stimulation mechanisms in enhanced geothermal systems. Int J Rock Mech Min Sci 72:242–260. https://doi.org/10.1016/j.ijrmms.2014.07.011CrossRef

Okada H, Higashi M, Kikuchi M, Fukui Y, Kumazawa N (2005) Three dimensional virtual crack closure-integral method (VCCM) with skewed and non-symmetric mesh arrangement at the crack front. Eng Fract Mech 72:1717–1737. https://doi.org/10.1016/j.engfracmech.2004.12.005CrossRef

Oore M, Burns DJ (1980) Estimation of stress intensity factors for irregular cracks subjected to arbitrary normal stress fields. Trans ASME 102:202–221. https://doi.org/10.1115/1.3263321CrossRef

Orifici AC, Thomson RS, Degenhardt R, Bisagni C, Bayandor J (2007) Development of a finite-element analysis methodology for the propagation of delaminations in composite structures. Mech Compos Mater 43(1):9–28. https://doi.org/10.1007/s11029-007-0002-6CrossRef

Parks DM (1974) A stiffness derivative finite element technique for determination of crack tip stress intensity factors. Int J Fract 10(4):487–502. https://doi.org/10.1007/BF00155252CrossRef

Parks DM (1977) The virtual crack extension method for nonlinear material behavior. Comput Methods Appl Mech Eng 12:353–364. https://doi.org/10.1016/0045-7825(77)90023-8CrossRef

Pietropaoli E, Riccio A (2010) On the robustness of finite element procedures based on virtual crack closure technique and fail release approach for delamination growth phenomena. Definition and assessment of a novel methodology. Compos Sci Technol 70(8):1288–1300. https://doi.org/10.1016/j.compscitech.2010.04.006CrossRef

Pietropaoli E, Riccio A (2011) Formulation and assessment of an enhanced finite element procedure for the analysis of delamination growth phenomena in composite structures. Compos Sci Technol 71(6):836–846. https://doi.org/10.1016/j.compscitech.2011.01.026CrossRef

Raju IS (1987) Calculation of strain-energy release rates with higher order and singular finite elements. Eng Fract Mech 28(3):251–274. https://doi.org/10.1016/0013-7944(87)90220-7CrossRef

Raju IS, Sistla R, Krishnamurthy T (1996) Fracture mechanics analyses for skin-stiffener debonding. Eng Fract Mech 54(3):371–385. https://doi.org/10.1016/0013-7944(95)00184-0CrossRef

Riccio A, Raimondo A, Scaramuzzino F (2015) A robust numerical approach for the simulation of skin-stringer debonding growth in stiffened composite panels under compression. Compos B 71:131–142. https://doi.org/10.1016/j.compositesb.2014.11.007CrossRef

Rice JR (1968) A path independent integral and the approximate analysis of strain concentration by notches and cracks. J Appl Mech 35:379–386. https://doi.org/10.1115/1.3601206CrossRef

Rybicki EF, Kanninen MF (1977) A finite element calculation of stress intensity factors by a modified crack closure integral. Eng Fract Mech 9(4):931–938. https://doi.org/10.1016/0013-7944(77)90013-3CrossRef

Savitski A, Detournay E (2002) Propagation of a penny-shaped fluid-driven fracture in an impermeable rock: asymptotic solutions. Int J Solids Struct 39:6311–6337. https://doi.org/10.1016/S0020-7683(02)00492-4CrossRef

Settgast RR, Fu P, Walsh SDC, White JA, Annavarapu C, Ryerson FJ (2017) A fully coupled method for massively parallel simulation of hydraulically driven fractures in 3-dimensions. Int J Numer Anal Method Geomech 41:627–653. https://doi.org/10.1002/nag.2557CrossRef

Shivakumar KN, Tan PW, Newman JC (1988) A virtual crack-closure technique for calculating stress intensity factors for cracked three dimensional bodies. Int J Fract 36:43–50

Shokrieh MM, Rajabpour-Shirazi H, Heidari-Rarani M, Haghpanahi M (2012) Simulation of mode I delamination propagation in multidirectional composites with R-curve effects using VCCT method. Comput Mater Sci 65:66–73. https://doi.org/10.1016/j.commatsci.2012.06.025CrossRef

Sneddon IN (1946) The distribution of stress in the neighbourhood of a crack in an elastic solid. Proc R Soc London Ser A 187(1009):229–260. https://doi.org/10.1098/rspa.1946.0077CrossRef

Sneddon IN, Elliott H (1946) The opening of a griffith crack under internal pressure. Q Appl Math 4(3):262–267. http://www.jstor.org/stable/43633558CrossRef

Sneddon IN, Lowengrub M (1969) Crack problems in the classic theory of elasticity. John Wiley and Son, New York. https://doi.org/10.1002/zamm.19710510317CrossRef

Tada H, Paris PC, Irwin OR (1973) The stress analysis of cracks handbook. Wiley-Blackwell, Hoboken. https://doi.org/10.1115/1.801535CrossRef

Weaver J (1977) Three-dimensional crack analysis. Int J Solids Struct 13(4):321–330. https://doi.org/10.1016/0020-7683(77)90016-6CrossRef

Xie D, Biggers SB (2006) Strain energy release rate calculation for a moving delamination front of arbitrary shape based on the virtual crack closure technique. Part I: formulation and validation. Eng Fract Mech 73(6):771–785. https://doi.org/10.1016/j.engfracmech.2005.07.013CrossRef

Xu W, Li Y, Zhao J, Chen X, Rahman SS (2020) Simulation of a hydraulic fracture interacting with a cemented natural fracture using displacement discontinuity method and finite volume method. Rock Mech Rock Eng 53:3373–3382. https://doi.org/10.1007/s00603-020-02106-2CrossRef

Zhai Z, Fonseca E, Azad A, Cox B (2015) A new tool for multi-cluster and multi-well hydraulic fracture modeling. SPE-173367-MS. https://doi.org/10.2118/SPE-173367-MS

Titel: An Enhanced Virtual Crack Closure Technique for Stress Intensity Factor Calculation along Arbitrary Crack Fronts and the Application in Hydraulic Fracturing Simulation
verfasst von: Hui Wu
Randolph R. Settgast
Pengcheng Fu
Joseph P. Morris
Publikationsdatum: 23.03.2021
Verlag: Springer Vienna
Erschienen in: Rock Mechanics and Rock Engineering / Ausgabe 6/2021
Print ISSN: 0723-2632
Elektronische ISSN: 1434-453X
DOI: https://doi.org/10.1007/s00603-021-02428-9

Springer Professional

Abstract

Bitte loggen Sie sich ein, um Zugang zu Ihrer Lizenz zu erhalten.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Technik"

Weitere Artikel der Ausgabe 6/2021

Three-dimensional Criterion for Predicting Peak Shear Strength of Matched Discontinuities with Different Joint Wall Strengths

Predicting the Strength of Granitic Stones after Freeze–Thaw Cycles: Considering the Petrographic Characteristics and a New Approach Using Petro-Mechanical Parameter

Simulating Hydraulic Fracture Re-orientation in Heterogeneous Rocks with an Improved Discrete Element Method

Effect of Compaction Banding on the Hydraulic Properties of Porous Rock - Part II: Constitutive Description and Numerical Simulations

Investigation of Failure Mechanism of Inclined Coal Pillars: Numerical Modelling and Tensorial Statistical Analysis with Field Validations

Application of Particle Stiffness Fabric Tensor for Modeling Inherent Anisotropy in Rocks