PSI - Issue 18

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ScienceDirect

Procedia Structural Integrity 18 (2019) 268–273 Structural Integrity Procedia 00 (2019) 000–000 Structural Integrity Procedia 00 (2019) 000–000

www.elsevier.com / locate / procedia www.elsevier.com / locate / procedia

25th International Conference on Fracture and Structural Integrity Calculation of Stress Intensity Factors with an Analytical Enrichment of the Modified Crack Closure Integral 25th International Conference on Fracture and Structural Integrity Calculation of Stress Intensity Factors with an Analytical Enrichment of the Modified Crack Closure Integral

Johannes Scheel a, ∗ , Andreas Ricoeur a , Martin Krupka a a Institute of Mechanics, University of Kassel, Mo¨nchebergstr. 7, D-34125 Kassel, Germany Johannes Scheel a, ∗ , Andreas Ricoeur a , Martin Krupka a a Institute of Mechanics, University of Kassel, Mo¨nchebergstr. 7, D-34125 Kassel, Germany

© 2019 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the Gruppo Italiano Frattura (IGF) ExCo. Abstract In this work a novel approach for the calculation of stress intensity factors (SIF) is derived and numerical results prove its appro priateness. The approach adopts and extends the idea of the modified crack closure integral (MCCI), is very simple to implement and does not need special meshes, extrapolations or nodal reaction forces. By using an interpolation function for the crack face displacements and inserting the near tip field solution for the stresses, the crack closure integral is calculated in a closed form and with the Irwin relation the SIF of mode-I and II are determined, based just on a few prescribed nodal displacements on the crack faces. Various examples of plane structures with cracks are the basis of verification. The new approach, denoted as enriched modified crack closure integral (EMCCI), appears to provide appropriate results, so far verified for single mode I loading scenar ios. In particular, for structures with non-idealized loading and geometry, the EMCCI is more accurate than e. g. the displacement interpretation method (DIM), even though being just as simple and eluding its drawbacks. c 2019 The Authors. Published by Elsevier B.V. P er-review under responsibility of the Gruppo Italiano Frattura (IGF) ExCo. Keywords: Stress intensity factors; Modified crack closure integral; Crack tip loading Abstract In this work a novel approach for the calculation of stress intensity factors (SIF) is derived and numerical results prove its appro priateness. The approach adopts and extends the idea of the modified crack closure integral (MCCI), is very simple to implement and does not need special meshes, extrapolations or nodal reaction forces. By using an interpolation function for the crack face displacements and inserting the near tip field solution for the stresses, the crack closure integral is calculated in a closed form and with the Irwin relation the SIF of mode-I and II are determined, based just on a few prescribed nodal displacements on the crack faces. Various examples of plane structures with cracks are the basis of verification. The new approach, denoted as enriched modified crack closure integral (EMCCI), appears to provide appropriate results, so far verified for single mode I loading scenar ios. In particular, for structures with non-idealized loading and geometry, the EMCCI is more accurate than e. g. the displacement interpretation method (DIM), even though being just as simple and eluding its drawbacks. c 2019 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the Gruppo Italiano Frattura (IGF) ExCo. Keywords: Stress intensity factors; Modified crack closure integral; Crack tip loading Crack tip loading quantities are fundamental in fracture mechanics, being the basis of crack growth and deflection criteria. To calculate them, a lot of numerical methods with di ff erent accurateness, implementation e ff ort, compu tational cost, mesh requirements and post processing necessities have emerged. Energy balance integrals, like the J-integral (independently introduced by Rice (1968) and Cherepanov (1967)), are highly e ffi cient as they are very accurate and directly enable crack path prediction via the J-integral deflection criterion [Strifors (1974), Judt et al. (2015)]. Unfortunately, the implementation is quite time consuming and more sophisticated than with other numerical methods. The crack tip element method (CTEM) [Barsoum (1976)] also is comparatively accurate, however requires special crack tip elements, complicating the structure’s meshing, in particular regarding crack growth simulations. The displacement interpretation method (DIM), introduced by Chan et al. (1970), is the most simple way to determine stress intensity factors (SIF) numerically, however, due to the required extrapolation of nodal displacements towards Crack tip loading quantities are fundamental in fracture mechanics, being the basis of crack growth and deflection criteria. To calculate them, a lot of numerical methods with di ff erent accurateness, implementation e ff ort, compu tational cost, mesh requirements and post processing necessities have emerged. Energy balance integrals, like the J-integral (independently introduced by Rice (1968) and Cherepanov (1967)), are highly e ffi cient as they are very accurate and directly enable crack path prediction via the J-integral deflection criterion [Strifors (1974), Judt et al. (2015)]. Unfortunately, the implementation is quite time consuming and more sophisticated than with other numerical methods. The crack tip element method (CTEM) [Barsoum (1976)] also is comparatively accurate, however requires special crack tip elements, complicating the structure’s meshing, in particular regarding crack growth simulations. The displacement interpretation method (DIM), introduced by Chan et al. (1970), is the most simple way to determine stress intensity factors (SIF) numerically, however, due to the required extrapolation of nodal displacements towards 1. Introduction 1. Introduction

2452-3216  2019 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the Gruppo Italiano Frattura (IGF) ExCo. 10.1016/j.prostr.2019.08.163 ∗ Corresponding author. Tel.: + 49-561-804-2824 . E-mail address: j.scheel@uni-kassel.de 2210-7843 c 2019 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the Gruppo Italiano Frattura (IGF) ExCo. ∗ Corresponding author. Tel.: + 49-561-804-2824 . E-mail address: j.scheel@uni-kassel.de 2210-7843 c 2019 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the Gruppo Italiano Frattura (IGF) ExCo.