A method for growing multiple cracks without remeshing and its application to fatigue crack growth

Goangseup Zi, Jeong Hoon Song, Elisa Budyn, Sang Ho Lee, Ted Belytschko

Research output: Contribution to journalArticle

71 Citations (Scopus)

Abstract

A numerical model to analyse the growth and the coalescence of cracks in a quasibrittle cell containing multiple cracks is presented. The method is based on the extended finite element method in which discontinuous enrichment functions are added to the finite element approximation to take into account the presence of the cracks, so that it requires no remeshing. In order to describe the discontinuities only the tip enrichment and the step enrichment are used. The method does not require a special enrichment for the junction of two cracks and the junction is automatically captured by the combination of the step enrichments. The geometry of the cracks which is described implicitly by the level set method is independent of the finite element mesh. In the numerical example, linear elastic fracture mechanics is adopted to describe the behaviour of the cracks along with the Paris fatigue law and the intact bulk material is assumed to be elastic. The numerical results show that cracks can grow and interconnect with each other without remeshing as fatigue progresses and that the pattern of fatigue crack development converges with mesh refinement.

Original languageEnglish
Pages (from-to)901-915
Number of pages15
JournalModelling and Simulation in Materials Science and Engineering
Volume12
Issue number5
DOIs
Publication statusPublished - 2004 Sep 1

Fingerprint

Fatigue Crack Growth
Remeshing
Fatigue crack propagation
Crack
cracks
Cracks
Fatigue
Fatigue of materials
Extended Finite Element Method
Fatigue Crack
Mesh Refinement
Level Set Method
Fracture Mechanics
Coalescence
Interconnect
fracture mechanics
Finite Element Approximation
Fracture mechanics
Numerical models
Discontinuity

All Science Journal Classification (ASJC) codes

  • Modelling and Simulation
  • Materials Science(all)
  • Condensed Matter Physics
  • Mechanics of Materials
  • Computer Science Applications

Cite this

@article{047560b9288a4f95a2cf0b37282ed5b8,
title = "A method for growing multiple cracks without remeshing and its application to fatigue crack growth",
abstract = "A numerical model to analyse the growth and the coalescence of cracks in a quasibrittle cell containing multiple cracks is presented. The method is based on the extended finite element method in which discontinuous enrichment functions are added to the finite element approximation to take into account the presence of the cracks, so that it requires no remeshing. In order to describe the discontinuities only the tip enrichment and the step enrichment are used. The method does not require a special enrichment for the junction of two cracks and the junction is automatically captured by the combination of the step enrichments. The geometry of the cracks which is described implicitly by the level set method is independent of the finite element mesh. In the numerical example, linear elastic fracture mechanics is adopted to describe the behaviour of the cracks along with the Paris fatigue law and the intact bulk material is assumed to be elastic. The numerical results show that cracks can grow and interconnect with each other without remeshing as fatigue progresses and that the pattern of fatigue crack development converges with mesh refinement.",
author = "Goangseup Zi and Song, {Jeong Hoon} and Elisa Budyn and Lee, {Sang Ho} and Ted Belytschko",
year = "2004",
month = "9",
day = "1",
doi = "10.1088/0965-0393/12/5/009",
language = "English",
volume = "12",
pages = "901--915",
journal = "Modelling and Simulation in Materials Science and Engineering",
issn = "0965-0393",
publisher = "IOP Publishing Ltd.",
number = "5",

}

A method for growing multiple cracks without remeshing and its application to fatigue crack growth. / Zi, Goangseup; Song, Jeong Hoon; Budyn, Elisa; Lee, Sang Ho; Belytschko, Ted.

In: Modelling and Simulation in Materials Science and Engineering, Vol. 12, No. 5, 01.09.2004, p. 901-915.

Research output: Contribution to journalArticle

TY - JOUR

T1 - A method for growing multiple cracks without remeshing and its application to fatigue crack growth

AU - Zi, Goangseup

AU - Song, Jeong Hoon

AU - Budyn, Elisa

AU - Lee, Sang Ho

AU - Belytschko, Ted

PY - 2004/9/1

Y1 - 2004/9/1

N2 - A numerical model to analyse the growth and the coalescence of cracks in a quasibrittle cell containing multiple cracks is presented. The method is based on the extended finite element method in which discontinuous enrichment functions are added to the finite element approximation to take into account the presence of the cracks, so that it requires no remeshing. In order to describe the discontinuities only the tip enrichment and the step enrichment are used. The method does not require a special enrichment for the junction of two cracks and the junction is automatically captured by the combination of the step enrichments. The geometry of the cracks which is described implicitly by the level set method is independent of the finite element mesh. In the numerical example, linear elastic fracture mechanics is adopted to describe the behaviour of the cracks along with the Paris fatigue law and the intact bulk material is assumed to be elastic. The numerical results show that cracks can grow and interconnect with each other without remeshing as fatigue progresses and that the pattern of fatigue crack development converges with mesh refinement.

AB - A numerical model to analyse the growth and the coalescence of cracks in a quasibrittle cell containing multiple cracks is presented. The method is based on the extended finite element method in which discontinuous enrichment functions are added to the finite element approximation to take into account the presence of the cracks, so that it requires no remeshing. In order to describe the discontinuities only the tip enrichment and the step enrichment are used. The method does not require a special enrichment for the junction of two cracks and the junction is automatically captured by the combination of the step enrichments. The geometry of the cracks which is described implicitly by the level set method is independent of the finite element mesh. In the numerical example, linear elastic fracture mechanics is adopted to describe the behaviour of the cracks along with the Paris fatigue law and the intact bulk material is assumed to be elastic. The numerical results show that cracks can grow and interconnect with each other without remeshing as fatigue progresses and that the pattern of fatigue crack development converges with mesh refinement.

UR - http://www.scopus.com/inward/record.url?scp=4544311316&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=4544311316&partnerID=8YFLogxK

U2 - 10.1088/0965-0393/12/5/009

DO - 10.1088/0965-0393/12/5/009

M3 - Article

AN - SCOPUS:4544311316

VL - 12

SP - 901

EP - 915

JO - Modelling and Simulation in Materials Science and Engineering

JF - Modelling and Simulation in Materials Science and Engineering

SN - 0965-0393

IS - 5

ER -