A complex-variable virtual crack extension finite element method for elastic-plastic fracture mechanics

•This study presents a new approach to calculate the nonlinear energy release rate.•The method evaluates the derivative of the potential energy using a complex-variable FEM.•The method overcomes the path dependency and monotonic loading limitation of the J-integral.•The method remains robust all lev...

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Bibliographic Details
Published in:Engineering fracture mechanics Vol. 202; pp. 242 - 258
Main Authors: Montoya, Arturo, Ramirez-Tamayo, Daniel, Millwater, Harry, Kirby, Matthew
Format: Journal Article
Language:English
Published: New York Elsevier Ltd 15.10.2018
Elsevier BV
Subjects:
Complex variable finite element method
Contours
Crack propagation
Dependence
Derivatives
Elastic limit
Elasto-plastic fracture
Elastoplasticity
Energy release rate
Finite element analysis
Finite element method
Flux density
Fracture mechanics
J integral
Mathematical analysis
Mathematical models
Nonlinear analysis
Nonlinear fracture
Plastic deformation
Plastic properties
Potential energy
Robustness (mathematics)
Series expansion
Shape
Taylor series
Virtual crack extension method
Virtual crack extension method
Complex variable finite element method
Energy release rate
Nonlinear fracture
Elasto-plastic fracture
ISSN:0013-7944, 1873-7315
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Summary:•This study presents a new approach to calculate the nonlinear energy release rate.•The method evaluates the derivative of the potential energy using a complex-variable FEM.•The method overcomes the path dependency and monotonic loading limitation of the J-integral.•The method remains robust all levels of plasticity, i.e. small, contained, and large scale yielding.•The method is superior to the J-integral when unloading from a yield state. The virtual crack extension (VCE) approach for computing the energy release rate using a complex-variable finite element method (ZFEM) is extended to nonlinear materials undergoing plastic deformation. The method consists of performing a numerical derivative of the potential energy with respect to a crack extension via the complex Taylor series expansion method (CTSE). ZFEM does not depend on the existence of a strain energy density and does not require contour or domain integrals. As a result, ZFEM overcomes the contour path dependency and monotonic loading limitations of the J-integral in elastic-plastic fracture problems. The nonlinear fracture analysis capability is demonstrated using material models based on the deformation and incremental theory of plasticity and using a loading/unloading cycle. Under monotonic loading, the ZFEM method remains robust at all levels of plasticity and its results are of the same accuracy as those provided by the ASTM standards and the saturated J-integral value. Moreover, when unloading the elasto-plastic material, the J-integral contours provide erroneous energy release rate values, whereas ZFEM results are in excellent agreement with those obtained by finite differencing.
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ISSN:0013-7944
1873-7315
DOI:10.1016/j.engfracmech.2018.09.023