### Abstract

When two-dimensional or three-dimensional elasticity theory is applied to interfacial cracks, individual components of the energy-release rate are not well defined in their classical crack closure integral form due to oscillatory stress and displacement fields around crack tips. These are associated with physically inadmissible interpenetration of crack surfaces. When dealing with composite laminates, it is generally preferable to use a laminate theory. However, when applied to delaminations most laminate models can only produce a total energy-release rate but not the individual components of it.

In this paper, expressions for individual energy-release rates have been derived for delaminations based on a sublaminate model. By considering delamination growth as a variational problem with variable endpoints, the total energy-release rate can be expressed simply in terms of stress resultant jumps and the derivatives of relative displacements between the delamination surfaces at its tip. The mode I, mode II and mode III components of the energy-release rate are then determined according to their definitions. The use of laminate theory eliminates oscillatory behaviour along with the stress singularity encountered in two-dimensional or three-dimensional linear elastic fracture mechanics theory for this problem. Instead, the effect of the singular stress field is reflected in the stress resultant jumps across the delamination tip. The individual energy-release rates derived in this way are all well defined. The present approach shows significant advantages over the popular finite-element-based virtual crack closure technique used for delamination problems.

Original language | English |
---|---|

Pages (from-to) | 645-677 |

Number of pages | 32 |

Journal | Proceedings of the Royal Society of London - A Mathematical and Physical Sciences |

Volume | 458 |

Issue number | 2019 |

DOIs | |

Publication status | Published - Mar 2002 |

### Keywords

- delamination
- energy-release rates
- sublaminate theory
- laminated composites
- mixed mode problems
- STRESS INTENSITY FACTORS
- INTERFACE CRACK
- GROWTH
- PLATES
- MEDIA

### Cite this

*Proceedings of the Royal Society of London - A Mathematical and Physical Sciences*,

*458*(2019), 645-677. https://doi.org/10.1098/RSPA.2001.0884

**General expressions for energy release rates for delamination in composite laminates.** / Reid, Stephen R; Soden, P. D.; Zou, Z.; Li, S.

Research output: Contribution to journal › Article

*Proceedings of the Royal Society of London - A Mathematical and Physical Sciences*, vol. 458, no. 2019, pp. 645-677. https://doi.org/10.1098/RSPA.2001.0884

}

TY - JOUR

T1 - General expressions for energy release rates for delamination in composite laminates

AU - Reid, Stephen R

AU - Soden, P. D.

AU - Zou, Z.

AU - Li, S.

PY - 2002/3

Y1 - 2002/3

N2 - When two-dimensional or three-dimensional elasticity theory is applied to interfacial cracks, individual components of the energy-release rate are not well defined in their classical crack closure integral form due to oscillatory stress and displacement fields around crack tips. These are associated with physically inadmissible interpenetration of crack surfaces. When dealing with composite laminates, it is generally preferable to use a laminate theory. However, when applied to delaminations most laminate models can only produce a total energy-release rate but not the individual components of it.In this paper, expressions for individual energy-release rates have been derived for delaminations based on a sublaminate model. By considering delamination growth as a variational problem with variable endpoints, the total energy-release rate can be expressed simply in terms of stress resultant jumps and the derivatives of relative displacements between the delamination surfaces at its tip. The mode I, mode II and mode III components of the energy-release rate are then determined according to their definitions. The use of laminate theory eliminates oscillatory behaviour along with the stress singularity encountered in two-dimensional or three-dimensional linear elastic fracture mechanics theory for this problem. Instead, the effect of the singular stress field is reflected in the stress resultant jumps across the delamination tip. The individual energy-release rates derived in this way are all well defined. The present approach shows significant advantages over the popular finite-element-based virtual crack closure technique used for delamination problems.

AB - When two-dimensional or three-dimensional elasticity theory is applied to interfacial cracks, individual components of the energy-release rate are not well defined in their classical crack closure integral form due to oscillatory stress and displacement fields around crack tips. These are associated with physically inadmissible interpenetration of crack surfaces. When dealing with composite laminates, it is generally preferable to use a laminate theory. However, when applied to delaminations most laminate models can only produce a total energy-release rate but not the individual components of it.In this paper, expressions for individual energy-release rates have been derived for delaminations based on a sublaminate model. By considering delamination growth as a variational problem with variable endpoints, the total energy-release rate can be expressed simply in terms of stress resultant jumps and the derivatives of relative displacements between the delamination surfaces at its tip. The mode I, mode II and mode III components of the energy-release rate are then determined according to their definitions. The use of laminate theory eliminates oscillatory behaviour along with the stress singularity encountered in two-dimensional or three-dimensional linear elastic fracture mechanics theory for this problem. Instead, the effect of the singular stress field is reflected in the stress resultant jumps across the delamination tip. The individual energy-release rates derived in this way are all well defined. The present approach shows significant advantages over the popular finite-element-based virtual crack closure technique used for delamination problems.

KW - delamination

KW - energy-release rates

KW - sublaminate theory

KW - laminated composites

KW - mixed mode problems

KW - STRESS INTENSITY FACTORS

KW - INTERFACE CRACK

KW - GROWTH

KW - PLATES

KW - MEDIA

U2 - 10.1098/RSPA.2001.0884

DO - 10.1098/RSPA.2001.0884

M3 - Article

VL - 458

SP - 645

EP - 677

JO - Proceedings of the Royal Society of London - A Mathematical and Physical Sciences

JF - Proceedings of the Royal Society of London - A Mathematical and Physical Sciences

SN - 0080-4630

IS - 2019

ER -