Full three dimensional cavitation instabilities using a non-quadratic anisotropic yield function

Brian Nyvang Legarth*, Viggo Tvergaard

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

Abstract

Full three dimensional cell models containing a small cavity are used to study the effect of plastic anisotropy on cavitation instabilities. Predictions for the Barlat-91 model (Int. J. Plast. 7, 693-712, 1991), with a non-quadratic anisotropic yield function, are compared with previous results for the classical anisotropic Hill-48 quadratic yield function (Proc. Royal Soc. Lond. A193, 281-297, 1948). The critical stress, at which the stored elastic energy will drive the cavity growth, is strongly affected by the anisotropy as compared to isotropic plasticity, but does not show much difference between the two models of anisotropy. While a cavity tends to remain nearly spherical during a cavitation instability in isotropic plasticity, the cavity shapes in an anisotropic material develop towards near-spheroidal elongated shapes, which differ for different values of the coefficients defining the anisotropy. The shapes found for the Barlat-91 model, with a non-quadratic anisotropic yield function, differ noticeably from the shapes found for the quadratic Hill-48 yield function. Computations are included for a high value of the exponent in the Barlat-91 model, where this model represents a Tresca-like yield surface with rounded corners.
Original languageEnglish
Article number031009
JournalJournal of Applied Mechanics
Volume87
Issue number3
Number of pages10
ISSN0021-8936
DOIs
Publication statusPublished - 2020

Keywords

  • Computational mechanics
  • Micromechanics
  • Plasticity
  • Stress analysis

Cite this

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title = "Full three dimensional cavitation instabilities using a non-quadratic anisotropic yield function",
abstract = "Full three dimensional cell models containing a small cavity are used to study the effect of plastic anisotropy on cavitation instabilities. Predictions for the Barlat-91 model (Int. J. Plast. 7, 693-712, 1991), with a non-quadratic anisotropic yield function, are compared with previous results for the classical anisotropic Hill-48 quadratic yield function (Proc. Royal Soc. Lond. A193, 281-297, 1948). The critical stress, at which the stored elastic energy will drive the cavity growth, is strongly affected by the anisotropy as compared to isotropic plasticity, but does not show much difference between the two models of anisotropy. While a cavity tends to remain nearly spherical during a cavitation instability in isotropic plasticity, the cavity shapes in an anisotropic material develop towards near-spheroidal elongated shapes, which differ for different values of the coefficients defining the anisotropy. The shapes found for the Barlat-91 model, with a non-quadratic anisotropic yield function, differ noticeably from the shapes found for the quadratic Hill-48 yield function. Computations are included for a high value of the exponent in the Barlat-91 model, where this model represents a Tresca-like yield surface with rounded corners.",
keywords = "Computational mechanics, Micromechanics, Plasticity, Stress analysis",
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language = "English",
volume = "87",
journal = "Journal of Applied Mechanics",
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Full three dimensional cavitation instabilities using a non-quadratic anisotropic yield function. / Legarth, Brian Nyvang; Tvergaard, Viggo.

In: Journal of Applied Mechanics, Vol. 87, No. 3, 031009, 2020.

Research output: Contribution to journalJournal articleResearchpeer-review

TY - JOUR

T1 - Full three dimensional cavitation instabilities using a non-quadratic anisotropic yield function

AU - Legarth, Brian Nyvang

AU - Tvergaard, Viggo

PY - 2020

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N2 - Full three dimensional cell models containing a small cavity are used to study the effect of plastic anisotropy on cavitation instabilities. Predictions for the Barlat-91 model (Int. J. Plast. 7, 693-712, 1991), with a non-quadratic anisotropic yield function, are compared with previous results for the classical anisotropic Hill-48 quadratic yield function (Proc. Royal Soc. Lond. A193, 281-297, 1948). The critical stress, at which the stored elastic energy will drive the cavity growth, is strongly affected by the anisotropy as compared to isotropic plasticity, but does not show much difference between the two models of anisotropy. While a cavity tends to remain nearly spherical during a cavitation instability in isotropic plasticity, the cavity shapes in an anisotropic material develop towards near-spheroidal elongated shapes, which differ for different values of the coefficients defining the anisotropy. The shapes found for the Barlat-91 model, with a non-quadratic anisotropic yield function, differ noticeably from the shapes found for the quadratic Hill-48 yield function. Computations are included for a high value of the exponent in the Barlat-91 model, where this model represents a Tresca-like yield surface with rounded corners.

AB - Full three dimensional cell models containing a small cavity are used to study the effect of plastic anisotropy on cavitation instabilities. Predictions for the Barlat-91 model (Int. J. Plast. 7, 693-712, 1991), with a non-quadratic anisotropic yield function, are compared with previous results for the classical anisotropic Hill-48 quadratic yield function (Proc. Royal Soc. Lond. A193, 281-297, 1948). The critical stress, at which the stored elastic energy will drive the cavity growth, is strongly affected by the anisotropy as compared to isotropic plasticity, but does not show much difference between the two models of anisotropy. While a cavity tends to remain nearly spherical during a cavitation instability in isotropic plasticity, the cavity shapes in an anisotropic material develop towards near-spheroidal elongated shapes, which differ for different values of the coefficients defining the anisotropy. The shapes found for the Barlat-91 model, with a non-quadratic anisotropic yield function, differ noticeably from the shapes found for the quadratic Hill-48 yield function. Computations are included for a high value of the exponent in the Barlat-91 model, where this model represents a Tresca-like yield surface with rounded corners.

KW - Computational mechanics

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KW - Plasticity

KW - Stress analysis

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