PSI - Issue 28

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ScienceDirect

Procedia Structural Integrity 28 (2020) 2350–2369 Structural Integrity Procedia 00 (2020) 000–000 Structural Integrity Procedia 0 (20 0) 00–000

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© 2020 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of the European Structural Integrity Society (ESIS) ExCo Abstract In some circumstances, the standard formulation of the virtual crack closure technique (VCCT) may yield negative values of the modal contributions to the energy release rate. To avoid such physically meaningless results, a revised formulation is available. However, the revised VCCT does not take into account possible interpenetration of the crack faces, that may be predicted by the linearly elastic solution. The present work extends the revised VCCT formulation by introducing suitable contact constraints to prevent local interpenetration of the crack-tip nodes. By considering open vs. interpenetrated cracks and tensile vs. compressive crack-tip forces, four cases emerge. For each case, a suitable two-step crack closure process is outlined with the two steps re spectively corresponding to fracture modes II and I. The contact pressure force, if present, is evaluated and accounted for in the computation of the crack closure work. As a result, novel analytical expressions are derived for the modal contributions to the energy release rate accounting for contact and prevented interpenetration. c 2020 The Authors. Published by Elsevier B.V. is is an open access article under the CC BY-NC-ND license (http: // creativec mmons.org / licenses / by-nc-nd / 4.0 / ) e r-review unde responsibility of the European St uctural Integr ty Society (ESIS) ExCo. Keywords: 1st Virtual European Conference on Fracture A physically consistent virtual crack closure technique accounting for contact and interpenetration Paolo S. Valvo a, ∗ a University of Pisa, Department of Civil and Industrial Engineering, Largo Lucio Lazzarino, I-56122 Pisa, PI, Italy Abstract In some circumstances, the standard formulation of the virtual crack closure technique (VCCT) may yield negative values of the modal contributions to the energy release rate. To avoid such physically meaningless results, a revised formulation is available. However, the revised VCCT does not take into account possible interpenetration of the crack faces, that may be predicted by the linearly elastic solution. The present work extends the revised VCCT formulation by introducing suitable contact constraints to prevent local interpenetration of the crack-tip nodes. By considering open vs. interpenetrated cracks and tensile vs. compressive crack-tip forces, four cases emerge. For each case, a suitable two-step crack closure process is outlined with the two steps re spectively corresponding to fracture modes II and I. The contact pressure force, if present, is evaluated and accounted for in the computation of the crack closure work. As a result, novel analytical expressions are derived for the modal contributions to the energy release rate accounting for contact and prevented interpenetration. c 2020 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http: // creativecommons.org / licenses / by-nc-nd / 4.0 / ) Peer-review under responsibility of the European Structural Integrity Society (ESIS) ExCo. Keywords: 1st Virtual European Conference on Fracture A physically consistent virtual crack closure technique accounting for contact and interpenetration Paolo S. Valvo a, ∗ a University of Pisa, Department of Civil and Industrial Engineering, Largo Lucio Lazzarino, I-56122 Pisa, PI, Italy

1. Introduction 1. Introduction

The virtual crack closure technique (VCCT) is a numerical method used to compute the energy release rate, G , in the finite element analysis of fracture mechanics problems [Krueger (2004)]. The technique was introduced first for two-dimensional problems by Rybicki and Kanninen (1977). Later, the VCCT was extended to three-dimensional problems by Shivakumar et al. (1988). For mixed-mode fracture problems, such as the delamination of composite materials and interfacial fracture, the VCCT furnishes not only the total G , but also the contributions, G I , G II , and G III , associated to the three basic fracture modes [Krueger et al. (2013)]. The virtual crack closure technique (VCCT) is a numerical method used to compute the energy release rate, G , in the finite element analysis of fracture mechanics problems [Krueger (2004)]. The technique was introduced first for two-dimensional problems by Rybicki and Kanninen (1977). Later, the VCCT was extended to three-dimensional problems by Shivakumar et al. (1988). For mixed-mode fracture problems, such as the delamination of composite materials and interfacial fracture, the VCCT furnishes not only the total G , but also the contributions, G I , G II , and G III , associated to the three basic fracture modes [Krueger et al. (2013)].

2452-3216 © 2020 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of the European Structural Integrity Society (ESIS) ExCo 10.1016/j.prostr.2020.11.083 ∗ Corresponding author. Tel.: + 39-050-2218223. E-mail address: p.valvo@ing.unipi.it 2210-7843 c 2020 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http: // creativecommons.org / licenses / by-nc-nd / 4.0 / ) Peer-review u der responsibility of the European Structural Integrity Society (ESIS) ExCo. ∗ Corresponding author. Tel.: + 39-050-2218223. E-mail address: p.valvo@ing.unipi.it 2210-7843 c 2020 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http: // creativecommons.org / licenses / by-nc-nd / 4.0 / ) Peer-review under responsibility of the European Structural Integrity Society (ESIS) ExCo.