Skip to main content
SpringerLink
Log in

The Role of Energetic and Dissipative Length Parameters

  • Chapter
  • First Online:
Strain Gradient Plasticity-Based Modeling of Damage and Fracture

Part of the book series: Springer Theses ((Springer Theses))

  • 754 Accesses

Abstract

Introduced by Gudmundson (J Mech Phys Solids 52:1379–1406, 2004, [1]) (see also the works by Gurtin (J Mech Phys Solids 52:2545–2568, 2004, [2]) and Gurtin and Anand (J Mech Phys Solids 53:1624–1649, 2005, [3]) to ensure positive plastic dissipation, energetic (or recoverable) and dissipative (or unrecoverable) gradient contributions are a common feature among the vast majority of the most recent SGP formulations. Two different gradient plasticity models are employed to assess the role of energetic and dissipative length parameters in fracture problems. The analysis of crack tip fields within a stationary crack reveals that both energetic and dissipative length scales lead to the same qualitative response, with their role weighted by the different constitutive prescriptions employed to account for the effect of GNDs. Larger differences arise when crack growth resistance is modeled by means of a cohesive zone formulation. The material response after crack initiation is therefore sensitive to the identification of the gradient contributions as energetic or dissipative.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Gudmundson P (2004) A unified treatment of strain gradient plasticity. J Mech Phys Solids 52:1379–1406. doi:10.1016/j.jmps.2003.11.002

    Article  MathSciNet  MATH  Google Scholar 

  2. Gurtin ME (2004) A gradient theory of small-deformation isotropic plasticity that accounts for the Burgers vector and for dissipation due to plastic spin. J Mech Phys Solids 52:2545–2568. doi:10.1016/j.jmps.2004.04.010

    Article  MathSciNet  MATH  Google Scholar 

  3. Gurtin ME, Anand L (2005) A theory of strain-gradient plasticity for isotropic, plastically irrotational materials. Part I: small deformations. J Mech Phys Solids 53:1624–1649. doi:10.1016/j.jmps.2004.12.008

    Article  MathSciNet  MATH  Google Scholar 

  4. Fleck NA, Willis JR (2009) A mathematical basis for straingradient plasticity theory-Part I: scalar plastic multiplier. J Mech Phys Solids 57:161–177. doi:10.1016/j.jmps.2008.09.010

    Article  MathSciNet  MATH  Google Scholar 

  5. Gurtin ME (2000) On the plasticity of single crystals: free energy, microforces, plastic-strain gradients. J Mech Phys Solids 48:989–1036. doi:10.1016/S0022-5096(99)00059-9

    Article  MathSciNet  MATH  Google Scholar 

  6. Anand L, Gurtin M, Lele S, Gething C (2005) A onedimensional theory of strain-gradient plasticity: formulation, analysis, numerical results. J Mech Phys Solids 53:1789–1826. doi:10.1016/j.jmps.2005.03.003

    Article  MathSciNet  MATH  Google Scholar 

  7. Fredriksson P, Gudmundson P (2005) Size-dependent yield strength of thin films. Int J Plast 21:1834–1854. doi:10.1016/j.ijplas.2004.09.005

    Article  MATH  Google Scholar 

  8. Bardella L (2010) Size effects in phenomenological strain gradient plasticity constitutively involving the plastic spin. Int J Eng Sci 48:550–568. doi:10.1016/j.ijengsci.2010.01.003

    Article  MathSciNet  MATH  Google Scholar 

  9. Niordson CF, Legarth BN (2010) Strain gradient effects on cyclic plasticity. J Mech Phys Solids 58:542–557. doi:10.1016/j.jmps.2010.01.007

    Article  MathSciNet  MATH  Google Scholar 

  10. Fleck NA, Muller GM, Ashby MF, Hutchinson JW (1994) Strain gradient plasticity: theory and experiment. Acta Metall Mater 42:457–487. doi:10.1016/0956-7151(94)90502-9

    Google Scholar 

  11. Swadener JG, George EP, Pharr GM (2002) The correlation of the indentation size effect measured with indenters of various shapes. J Mech Phys Solids 50:681–694. doi:10.1016/S0022-5096(01)00103-X

    Article  MATH  Google Scholar 

  12. Stölken JS, Evans AG (1998) A microbend test method for measuring the plasticity length scale. Acta Mater 46:5109–5115. doi:10.1016/S1359-6454(98)00153-0

  13. Xiang Y, Vlassak JJ (2006) Bauschinger and size effects in thinfilm plasticity. J Mech Phys Solids 54:5449–5460. doi:10.1016/j.actamat.2006.06.059

    Google Scholar 

  14. Haque MA, Saif MTA (2003) Strain gradient effect in nanoscale thin films. Acta Mater 51:3053–3061. doi:10.1016/S1359-6454(03)00116-2

    Article  Google Scholar 

  15. Voyiadjis GZ, Al-Rub RKA (2005) Gradient plasticity theory with a variable length scale parameter. Int J Solids Struct 42:3998–4029. doi:10.1016/j.ijsolstr.2004.12.010

    Article  MATH  Google Scholar 

  16. Bardella L, Panteghini A (2015) Modelling the torsion of thin metal wires by distortion gradient plasticity. J Mech Phys Solids 78:467–492. doi:10.1016/j.jmps.2015.03.003

    Article  MathSciNet  MATH  Google Scholar 

  17. Danas K, Deshpande VS, Fleck NA (2012) Size effects in the conical indentation of an elasto-plastic solid. J Mech Phys Solids 60:1605–1625. doi:10.1016/j.jmps.2012.05.002

    Article  MathSciNet  Google Scholar 

  18. Nye JF (1953) Some geometrical relations in dislocated crystals. Acta Metall 1:153–162. doi:10.1016/0001-6160(53)90054-6

    Article  Google Scholar 

  19. Martínez-Pañeda E, Niordson CF, Bardella L (2016) A finite element framework for distortion gradient plasticity with applications to bending of thin foils. Int J Solids Struct 96:288–299. doi:10.1016/j.ijsolstr.2016.06.001

  20. Forest S, Guéninchault N (2013) Inspection of free energy functions in gradient crystal plasticity. Acta Mechanica Sin 29: 763–772. doi:10.1007/s10409-013-0088-0

  21. Tvergaard V, Hutchinson JW (1992) The relation between crack growth resistance and fracture process parameters in elastic-plastic solids. J Mech Phys Solids 40:1377–1397. doi:10.1016/0022-5096(92)90020-3

    Article  MATH  Google Scholar 

  22. Xu X-P, Needleman A (1999) Void nucleation by inclusion debonding in a crystal matrix. Model Simul Mater Sci Eng 1:111–132. doi:10.1088/0965-0393/1/2/001

    Article  Google Scholar 

  23. Deshpande VS, Needleman A, Van der Giessen E (2002) Discrete dislocation modeling of fatigue crack propagation. Acta Mater 50:831–846. doi:10.1016/S1359-6454(01)00377-9

    Article  Google Scholar 

  24. Tvergaard V, Niordson CF, Hutchinson JW (2013) Material size effects on crack growth along patterned wafer-level Cu-Cu bonds. Int J Mech Sci 68:270–276. doi:10.1016/j.ijmecsci.2013.01.027

    Article  Google Scholar 

  25. Schellekens JCJ, de Borst R (1993) On the numerical integration of interface elements. Int J Numer Methods Eng 36:43–66. doi:10.1002/nme.1620360104

    Article  MATH  Google Scholar 

  26. Camacho GT, Ortiz M (1996) Computational modelling of impact damage in brittle materials. Int J Solids Struct 33:2899–2938. doi:10.1016/0020-7683(95)00255-3

    Article  MATH  Google Scholar 

  27. Tvergaard V (1976) Effect of thickness inhomogeneities in internally pressurized elastic-plastic spherical shells. J Mech Phys Solids 24:291–304. doi:10.1016/0022-5096(76)90027-2

    Article  Google Scholar 

  28. Segurado J, Llorca J (2004) A new three-dimensional interface finite element to simulate fracture in composites. Int J Solids Struct 41:2977–2993. doi:10.1016/j.ijsolstr.2004.01.007

    Article  MATH  Google Scholar 

  29. Lemonds J, Needleman A (1986) Finite element analyses of shear localization in rate and temperature dependent solids. Mech Mater 5:339–361. doi:10.1016/0167-6636(86)90039-6

    Article  Google Scholar 

  30. Chowdhury SR, Narasimhan R (2000) A cohesive finite element formulation for modelling fracture and delamination in solids. Sadhana 25:561–587. doi:10.1007/BF02703506

    Article  Google Scholar 

  31. del Busto S, Betegón C, Martínez-Pañeda E (2017, in press) A cohesive zone framework for environmentally assisted fatigue. Eng Fract Mech. doi:10.1016/j.engfracmech.2017.05.021

  32. Fleck NA, Willis JR (2015) Strain gradient plasticity: energetic or dissipative? Acta Mech Sin 31:465–472. doi:10.1007/s10409-015-0468-8

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Construction and Manufacturing Engineering, University of Oviedo, Gijón, Spain

    Emilio Martínez Pañeda

Authors
  1. Emilio Martínez Pañeda
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Emilio Martínez Pañeda .

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer International Publishing AG

About this chapter

Cite this chapter

Martínez Pañeda, E. (2018). The Role of Energetic and Dissipative Length Parameters. In: Strain Gradient Plasticity-Based Modeling of Damage and Fracture. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-63384-8_6

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-63384-8_6

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-63383-1

  • Online ISBN: 978-3-319-63384-8

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation