PSI - Issue 28

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ScienceDirect

Procedia Structural Integrity 28 (2020) 2320–2327 Structural Integrity Procedia 00 (2020) 000–000 Structural Integrity Procedia 0 (20 0) 00–000

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1st Virtual European Conference on Fracture Energy characteristics of interfacial bridged cracks Mikhail Perelmuter ∗ Ishlinsky Institute for Problems in Mechanics RAS, Vernadsky avenue 101-1, Moscow, 119526, Russia 1st Virtual European Conference on Fracture Energy characteristics of interfacial bridged cracks Mikhail Perelmuter ∗ Ishlinsky Institute for Problems in Mechanics RAS, Vernadsky avenue 101-1, Moscow, 119526, Russia

© 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 Two energy characteristics of interfacial bridged cracks are considered: 1) the deformation energy release rate associated with the crack tip stress intensity factors; 2) the rate of the energy absorbtion by bonds associated with the energy necessary to create a unit of new surface of the bridged zone. The analysis of these energy characteristics (the last one - with more details) for interfacial straight bridged crack is performed numerically. The influence of materials and bonds mechanical properties on the energy characteristics of the bridged crack is studied. The limit equilibrium analysis of a crack is performed on the basis of the proposed nonlocal two-parametrical fracture criterion with the crack tip development condition which is based on the crack bridged zone energy characteristics (it is the necessary fracture condition) and the kinematic condition for the advancing of the trailing edge of the crack bridged zone (it is the su ffi cient fracture condition). The regimes of the equilibrium and quasi-static growth of the bridged zone and the crack tip are formulated. 2020 The Authors. Published by Elsevier B.V. T is is an open access article under the CC BY- C-ND license (http: // cr ativec mmons.org / licenses / by-nc-nd / 4.0 / ) P r ie unde responsibility of the European St uctural Integrity Society (ESIS) ExCo. Keywords: bridged crack; deformation energy release rate; rate of the energy absorbtion by bonds; non-local fracture criterion Abstract Two energy characteristics of interfacial bridged cracks are considered: 1) the deformation energy release rate associated with the crack tip stress intensity factors; 2) the rate of the energy absorbtion by bonds associated with the energy necessary to create a unit of new surface of the bridged zone. The analysis of these energy characteristics (the last one - with more details) for interfacial straight bridged crack is performed numerically. The influence of materials and bonds mechanical properties on the energy characteristics of the bridged crack is studied. The limit equilibrium analysis of a crack is performed on the basis of the proposed nonlocal two-parametrical fracture criterion with the crack tip development condition which is based on the crack bridged zone energy characteristics (it is the necessary fracture condition) and the kinematic condition for the advancing of the trailing edge of the crack bridged zone (it is the su ffi cient fracture condition). The regimes of the equilibrium and quasi-static growth of the bridged zone and the crack tip are formulated. © 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: bridged crack; deformation energy release rate; rate of the energy absorbtion by bonds; non-local fracture criterion

1. Introduction 1. Introduction

Models of a crack with interaction of its faces make it possible to combine the approaches of fracture mechanics and physics of strength in the analysis of crack growth. Zones of the crack faces interaction (fracture process zones) are usually adjacent to the crack tips, where cohesion forces (adhesion in the case of di ff erent materials) are applied to the crack faces and restrain the crack opening, Barenblatt (1962). Di ff erent versions of fracture process zone models (“cohesive” or “bridged”) for analyzing brittle and elastic-plastic fracture of homogeneous bodies were proposed (see the reviews Bao and Suo (1992), Cox and Marshall (1994)). If several physical mechanisms are involved in the processes of deformation and rupture in the fracture process zone, as, for example, in composite materials, in such cases is more e ff ective to use the process zone models with the crack tips stresses singularity. Such models (in the terminology of Cox and Marshall (1994) these are bridged crack models) have been examined for cracks in Models of a crack with interaction of its faces make it possible to combine the approaches of fracture mechanics and physics of strength in the analysis of crack growth. Zones of the crack faces interaction (fracture process zones) are usually adjacent to the crack tips, where cohesion forces (adhesion in the case of di ff erent materials) are applied to the crack faces and restrain the crack opening, Barenblatt (1962). Di ff erent versions of fracture process zone models (“cohesive” or “bridged”) for analyzing brittle and elastic-plastic fracture of homogeneous bodies were proposed (see the reviews Bao and Suo (1992), Cox and Marshall (1994)). If several physical mechanisms are involved in the processes of deformation and rupture in the fracture process zone, as, for example, in composite materials, in such cases is more e ff ective to use the process zone models with the crack tips stresses singularity. Such models (in the terminology of Cox and Marshall (1994) these are bridged crack models) have been examined for cracks in

∗ Corresponding author. Tel.: + 7-495-433-6257; fax: + 7-499-739-9531. E-mail address: perelm@ipmnet.ru ∗ Corresponding author. Tel.: + 7-495-433-6257; fax: + 7-499-739-9531. E-mail address: perelm@ipmnet.ru

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.2020.11.079 2210-7843 © 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. 2210-7843 © 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.