International Journal of Fracture

, Volume 199, Issue 1, pp 89–104 | Cite as

Energy dissipation via acoustic emission in ductile crack initiation

  • J. A. Cuadra
  • K. P. Baxevanakis
  • M. Mazzotti
  • I. Bartoli
  • A. KontsosEmail author
Original Paper


This article presents a modeling approach to estimate the energy release due to ductile crack initiation in conjunction to the energy dissipation associated with the formation and propagation of transient stress waves typically referred to as acoustic emission. To achieve this goal, a ductile fracture problem is investigated computationally using the finite element method based on a compact tension geometry under Mode I loading conditions. To quantify the energy dissipation associated with acoustic emission, a crack increment is produced given a pre-determined notch size in a 3D cohesive-based extended finite element model. The computational modeling methodology consists of defining a damage initiation state from static simulations and linking such state to a dynamic formulation used to evaluate wave propagation and related energy redistribution effects. The model relies on a custom traction separation law constructed using full field deformation measurements obtained experimentally using the digital image correlation method. The amount of energy release due to the investigated first crack increment is evaluated through three different approaches both for verification purposes and to produce an estimate of the portion of the energy that radiates away from the crack source in the form of transient waves. The results presented herein propose an upper bound for the energy dissipation associated to acoustic emission, which could assist the interpretation and implementation of relevant nondestructive evaluation methods and the further enrichment of the understanding of effects associated with fracture.


Acoustic emission energy Cohesive zone modeling Extended finite element method Digital image correlation technique 



The results reported here were obtained by using computational resources supported by Drexel’s University Research Computing Facility. This material is also based upon work supported by the National Science Foundation Graduate Research Fellowship under Grant No. 1002809. In addition, A. Kontsos and I. Bartoli acknowledge the financial support received by the Office of Naval Research, Award N00014-13-1-0143.


  1. ABAQUS (2013) version 6.13, 2013. User’s Manual. Dassault Systems, Pawtucket, RIGoogle Scholar
  2. Achenbach J (1973) Wave propagation in elastic solids. North-Holland Publishing Company, AmsterdamGoogle Scholar
  3. Anderson TL (2005) Fracture mechanics: fundamentals and applications. CRC Press, Boca RatonGoogle Scholar
  4. ASTM E1820-01 (2001) Standard test method for measurement of fracture toughness, pp 1–46Google Scholar
  5. ASTM E1316-10c (2010) Standard terminology for nondestructive examinations. West Conshohocken, PAGoogle Scholar
  6. Auld BA (1973) Acoustic fields and waves in solids. I. Wiley-Interscience, New YorkGoogle Scholar
  7. Boler FM (1990) Measurements of radiated elastic wave energy from dynamic tensile cracks. J Geophys Res: Solid Earth 95:2593–2607CrossRefGoogle Scholar
  8. Bosia F, Pugno N, Lacidogna G, Carpinteri A (2008) Mesoscopic modeling of acoustic emission through an energetic approach. Int J Solids Struct 45:5856–5866CrossRefGoogle Scholar
  9. Boyce BL, Kramer SLB, Fang HE, Cordova TE, Neilsen MK, Dion K, Kaczmarowski AK, Karasz E, Xue L, Gross AJ, Ghahremaninezhad A, Ravi-Chandar K, Lin SP, Chi SW, Chen JS, Yreux E, Rüter M, Qian D, Zhou Z, Bhamare S, O’Connor DT, Tang S, Elkhodary KI, Zhao J, Hochhalter JD, Cerrone AR, Ingraffea AR, Wawrzynek PA, Carter BJ, Emery JM, Veilleux MG, Yang P, Gan Y, Zhang X, Chen Z, Madenci E, Kilic B, Zhang T, Fang E, Liu P, Lua J, Nahshon K, Miraglia M, Cruce J, DeFrese R, Moyer ET, Brinckmann S, Quinkert L, Pack K, Luo M, Wierzbicki T (2014) The Sandia fracture challenge: blind round robin predictions of ductile tearing. Int J Fract 186:5–68CrossRefGoogle Scholar
  10. Brocks W, Scheider I, Geesthacht G-F (2001) Numerical aspects of the path-dependence of the j-integral in incremental plasticity. GKSS Forschungszentrum, Geesthacht, Germany, Technical Report No. GKSS/WMS/01/08Google Scholar
  11. Carka D, Landis CM (2010) On the path-dependence of the J-integral near a stationary crack in an elastic-plastic material. J Appl Mech 78:011006CrossRefGoogle Scholar
  12. Cherepanov GP (1967) Crack propagation in continuous media: PMM vol. 31, no. 3, 1967, pp. 476–488. J Appl Math Mech 31:503–512Google Scholar
  13. Chung J-B, Kannatey-Asibo E (1992) Accoustic emission from plastic deformation of a pure single crystal. J Appl Phys 72:1812–1820Google Scholar
  14. Clarke G, Landes J (1979) Evaluation of the J integral for the compact specimen. J Test Evalu 7:264–269CrossRefGoogle Scholar
  15. Cuadra J, Vanniamparambil PA, Servansky D, Bartoli I, Kontsos A (2015) Acoustic emission source modeling using a data-driven approach. J Sound Vib 341:222–236CrossRefGoogle Scholar
  16. Döll W (1984) Kinetics of crack tip craze zone before and during fracture. Polym Eng Sci 24:798–808CrossRefGoogle Scholar
  17. Ernst H, Paris P, Rossow M, Hutchinson J (1979) Analysis of load-displacement relationship to determine J–R curve and tearing instability material properties. Fract Mech ASTM STP 677:581–599CrossRefGoogle Scholar
  18. Feih S (2006) Development of a user element in ABAQUS for modelling of cohesive laws in composite structures. Risø National Laboratory, Roskilde (Denmark), p 52Google Scholar
  19. Gain A, Carroll J, Paulino G, Lambros J (2011) A hybrid experimental/numerical technique to extract cohesive fracture properties for mode-I fracture of quasi-brittle materials. Int J Fract 169:113–131CrossRefGoogle Scholar
  20. Griffith AA (1921) The phenomena of rupture and flow in solids. Philos Trans R Soc Lond A Contain Papers Math Phys Character 221:163–198Google Scholar
  21. Gross SP, Fineberg J, Marder M, McCormick WD, Swinney HL (1993) Acoustic emissions from rapidly moving cracks. Phys Rev Lett 71:3162–3165CrossRefGoogle Scholar
  22. Hack JE, Chen SP, Srolovitz DJ (1989) A kinetic criterion for quasi-brittle fracture. Acta Metallurgica 37:1957–1970CrossRefGoogle Scholar
  23. Hora P, Črvená O, Uhnáková A, Machová A, Pelikán V (2013) Stress wave radiation from brittle crack extension by molecular dynamics and FEM. Appl Comput Mech 7:23–30Google Scholar
  24. Hutchinson JW (1968) Singular behaviour at the end of a tensile crack in a hardening material. J Mech Phys Solids 16:13–31Google Scholar
  25. Jungk JM, Boyce BL, Buchheit TE, Friedmann TA, Yang D, Gerberich WW (2006) Indentation fracture toughness and acoustic energy release in tetrahedral amorphous carbon diamond-like thin films. Acta Materialia 54:4043–4052CrossRefGoogle Scholar
  26. King R, Herrmann G, Kino GS (1981) Acoustic nondestructive evaluation of energy release rates in plane cracked solids. In: Proceedings of the DARPA/AFWAL review of progress in quantitative NDE, pp 38–43Google Scholar
  27. Koslowski M, LeSar R, Thomson R (2004) Avalanches and scaling in plastic deformation. Phys Rev Lett 93:125502Google Scholar
  28. Lamark TT, Chmelık F, Estrin Y, Luka P (2004) Cyclic deformation of a magnesium alloy investigated by the acoustic emission technique. J Alloys Compd 378:202–206CrossRefGoogle Scholar
  29. Li FZ, Shih CF, Needleman A (1985) A comparison of methods for calculating energy release rates. Eng Fract Mech 21:405–421CrossRefGoogle Scholar
  30. Lockner DA, Byerlee JD, Kuksenko V, Ponomarev A, Sidorin A (1991) Quasi-static fault growthand shear fracure energy in granite. Nature 350:39–42CrossRefGoogle Scholar
  31. Lou XY, Li M, Boger RK, Agnew SR, Wagoner RH (2007) Hardening evolution of AZ31B Mg sheet. Int J Plasticity 23:44–86CrossRefGoogle Scholar
  32. Mathis K, Chmelık F, Janecek M, Hadzima B, Trojanova Z, Luka P (2006) Investigating deformation processes in AM60 magnesium alloy using the acoustic emission technique. Acta Materialia 54:5361–5366CrossRefGoogle Scholar
  33. Merkle JG, Corten HT (1974) A J integral analysis for the compact specimen, considering axial force as well as bending effects. J Press Vessel Technol 96:286–292CrossRefGoogle Scholar
  34. Miguel M-C, Vespignani A, Zapperi S, Weiss§ J, Grasso J-R (2001) Intermittent dislocation flow in viscoplastic deformation. Nature 410:667–671CrossRefGoogle Scholar
  35. Moosbrugger C (2002) Atlas of stress-strain curves. ASM International, Materials ParkGoogle Scholar
  36. Muralidhara S, Prasad RB, Singh R (2013) Analysis of acoustic emission data to estimate true fracture energy of plain concrete. Curr Sci 105:1213–1216Google Scholar
  37. Nguyen O, Repetto EA, Ortiz M, Radovitzky RA (2001) A cohesive model of fatigue crack growth. Int J Fract 110:351–369CrossRefGoogle Scholar
  38. Owen DM, Zhuang S, Rosakis AJ, Ravichandran G (1998) Experimental determination of dynamic crack initiation and propagation fracture toughness in thin aluminum sheets. Int J Fract 90:153–174CrossRefGoogle Scholar
  39. Parks DM (1977) The virtual crack extension method for nonlinear material behavior. Comput Methods Appl Mech Eng 12:353–364CrossRefGoogle Scholar
  40. Ravi-Chandar K (2004) Dynamic fracture. Elsevier, AmsterdamGoogle Scholar
  41. Rice JR (1965) An examination of the fracture mechanics energy balance from the point of view of continuum mechanics, ICF1, JapanGoogle Scholar
  42. Rice JR (1968) A path independent integral and the approximate analysis of strain concentration by notches and cracks. J Appl Mech 35:379–386CrossRefGoogle Scholar
  43. Rice JR, Rosengren GF (1968) Plane strain deformation near a crack tip in a power-law hardening material. J Mech Phys Solids 16:1–12CrossRefGoogle Scholar
  44. Richeton T, Dobron P, Chmelik F, Weiss J, Louchet F (2006) On the critical character of plasticity in metallic single crystals. Mater Sci Eng A 424:190–195CrossRefGoogle Scholar
  45. Sause MGR, Müller T, Horoschenkoff A, Horn S (2012) Quantification of failure mechanisms in Mode-I loading of fiber reinforced plastics utilizing acoustic emission analysis. Compos Sci Technol 72:167–174CrossRefGoogle Scholar
  46. Sause MR, Richler S (2015) Finite element modelling of cracks as acoustic emission sources. J Nondestruct Eval 34:1–13CrossRefGoogle Scholar
  47. Sharon E, Gross SP, Fineberg J (1996) Energy dissipation in dynamic fracture. Phys Rev Lett 76:2117–2120CrossRefGoogle Scholar
  48. Shen B, Paulino GH (2011) Direct extraction of cohesive fracture properties from digital image correlation: a hybrid inverse technique. Exp Mech 51:143–163CrossRefGoogle Scholar
  49. Shih CF, Moran B, Nakamura T (1986) Energy release rate along a three-dimensional crack front in a thermally stressed body. Int J Fract 30:79–102Google Scholar
  50. Uhnáková A, Machová A, Hora P, Červ J, Kroupa T (2010) Stress wave radiation from the cleavage crack extension in 3D bcc iron crystals. Comput Mater Sci 50:678–685CrossRefGoogle Scholar
  51. van Bohemen SMC, Sietsma J, Hermans MJM, Richardson IM (2003) Kinetics of the martensitic transformation in low-alloy steel studied by means of acoustic emission. Acta Materialia 51:4183–4196CrossRefGoogle Scholar
  52. Vanniamparambil PA, Guclu U, Kontsos A (2015) Identification of crack initiation in aluminum alloys using acoustic emission. Exp Mech 55:837–850CrossRefGoogle Scholar
  53. Wisner B, Cabal M, Vanniamparambil PA, Hochhalter J, Leser WP, Kontsos A (2015) In situ microscopic investigation to validate acoustic emission monitoring. Exp Mech 55:1705–1715CrossRefGoogle Scholar
  54. Zhu Y, Liechti KM, Ravi-Chandar K (2009) Direct extraction of rate-dependent traction-separation laws for polyurea/steel interfaces. Int J Solids Struct 46:31–51CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  • J. A. Cuadra
    • 1
    • 3
  • K. P. Baxevanakis
    • 1
  • M. Mazzotti
    • 2
  • I. Bartoli
    • 2
  • A. Kontsos
    • 1
    Email author
  1. 1.Theoretical and Applied Mechanics Group, Mechanical Engineering and Mechanics DepartmentDrexel UniversityPhiladelphiaUSA
  2. 2.Civil, Architectural and Environmental Engineering DepartmentDrexel UniversityPhiladelphiaUSA
  3. 3.Lawrence Livermore National LaboratoryNondestructive Characterization InstituteLivermoreUSA

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