Computation of two dimensional mixed-mode stress intensity factor rates using a complex-variable interaction integral

The well-known interaction integral, also known as the M-integral or I-integral, is a method to compute the mixed-mode stress intensity factors (SIFs) for fracture mechanics problems. The capabilities of the M-integral are extended here to compute derivatives of the SIFs with respect to the crack ex...

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Bibliographic Details
Published in:Engineering fracture mechanics Vol. 277; p. 108981
Main Authors: Aguirre-Mesa, Andres M., Restrepo-Velasquez, Sara, Ramirez-Tamayo, Daniel, Montoya, Arturo, Millwater, Harry
Format: Journal Article
Language:English
Published: Elsevier Ltd 01.01.2023
Subjects:
Complex Taylor series expansion
Complex-variable finite element method
Interaction integral
M-integral
Complex Taylor series expansion
Complex-variable finite element method
M-integral
Interaction integral
ISSN:0013-7944, 1873-7315
Online Access:Get full text
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Summary:The well-known interaction integral, also known as the M-integral or I-integral, is a method to compute the mixed-mode stress intensity factors (SIFs) for fracture mechanics problems. The capabilities of the M-integral are extended here to compute derivatives of the SIFs with respect to the crack extensions for an isotropic linear elastic material under static loading. These derivatives were calculated using the complex Taylor series expansion (CTSE) numerical differentiation method. The derivatives of the auxiliary fields are calculated by applying CTSE directly to the M-integral formulation. The derivatives of the actual displacement fields are computed using a hypercomplex-variable finite element method (ZFEM) that also employs CTSE. SIF rates with respect to all crack tips are computed in a single analysis. The method is general and can be easily extended to other two-dimensional loading scenarios and different material models in a straightforward manner through the use of the appropriate auxiliary fields. The complex-variable M-integral was implemented within the commercial finite element software Abaqus through a user-defined element subroutine (UEL). Numerical examples demonstrate the high accuracy of the method. •Method to calculate stress intensity factor rates using a complex Taylor expansion.•The method is simple and does not involve any new integral formulations.•Rates with respect to the same crack tip and other crack tips are computed.•The method can be extended for derivatives over any material or geometric parameter.
ISSN:0013-7944
1873-7315
DOI:10.1016/j.engfracmech.2022.108981