PSI - Issue 25

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ScienceDirect

Procedia Structural Integrity 25 (2020) 268–281 Structural Integrity Procedia 00 (2019) 000–000 Structural Integrity Procedia 00 (2019) 000–000

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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 (http://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review under responsibility of the VCSI1 organizers Abstract Simplified mathematical models are extremely useful for understanding and characterizing physical phenomena; this is the case of plane (stress / strain) elasticity, which has been the main analytical framework of Fracture Mechanics since its origins. Bowed crack fronts in thin sheets and plates, unpredicted fatigue crack paths, and crack initiation as well as brittle fracture location are only examples of fracture mechanisms not completely explained by the classical closed form 2D solutions, e.g. Westergaard’s solution. This paper aims to provide a brief review on 3D e ff ects on the brittle fracture behavior of linear, elastic, homogeneous and isotropic solids in presence of cracks or notches, under the hypothesis of small scale plasticity (LEFM). We overview the main theoretical and numerical results on coupled modes of fracture, i.e. coupling of shear (Mode II) and out-of-plane (Mode III) modes, due to three-dimensional e ff ects and on 3D vertex singularities close to a corner point generated by the intersection of a crack / notch front with free surfaces. We also address recent theoretical-numerical studies and inconsistencies on the relation of crack (notch) tip stress singularities, usually characterized by local (notch) stress intensity factors, in the vicinity of a corner point and far away from it. Despite numerous works have attempted to interpret finite element and analytical results, no consensus exists on the behavior of the 3D stress field near a vertex of cracked / notched solids; a unifying theory, able to guarantee the extension of the results of experimental tests prescribed by standards, based on the 2D theory of elasticity, to real cases, is still required. c 2020 The Authors. Published by Elsevier B.V. T is an open access article under the CC BY- C-ND license (http: // creativecommons.org / licenses / by-nc-nd / 4.0 / ) P er-revie lin : Peer-rev ew und r responsibility of the VCSI1 organizers. Keywords: Fracture Mechanics; 3D e ff ects; coupled modes; stress singularities; vertex singularities; stress intensity factors 1st Virtual Conference on Structural Integrity – VCSI1 3D e ff ects on Fracture echanics Marco Maurizi a, ∗ , Filippo Berto a a NTNU - Norwegian University of Science and Technology –Department of Mechanical Engineering, 7491 Trondheim, Norway Abstract Simplified mathematical models are extremely useful for understanding and characterizing physical phenomena; this is the case of plane (stress / strain) elasticity, which has been the main analytical framework of Fracture Mechanics since its origins. Bowed crack fronts in thin sheets and plates, unpredicted fatigue crack paths, and crack initiation as well as brittle fracture location are only examples of fracture mechanisms not completely explained by the classical closed form 2D solutions, e.g. Westergaard’s solution. This paper aims to provide a brief review on 3D e ff ects on the brittle fracture behavior of linear, elastic, homogeneous and isotropic solids in presence of cracks or notches, under the hypothesis of small scale plasticity (LEFM). We overview the main theoretical and numerical results on coupled modes of fracture, i.e. coupling of shear (Mode II) and out-of-plane (Mode III) modes, due to three-dimensional e ff ects and on 3D vertex singularities close to a corner point generated by the intersection of a crack / notch front with free surfaces. We also address recent theoretical-numerical studies and inconsistencies on the relation of crack (notch) tip stress singularities, usually characterized by local (notch) stress intensity factors, in the vicinity of a corner point and far away from it. Despite numerous works have attempted to interpret finite element and analytical results, no consensus exists on the behavior of the 3D stress field near a vertex of cracked / notched solids; a unifying theory, able to guarantee the extension of the results of experimental tests prescribed by standards, based on the 2D theory of elasticity, to real cases, is still required. 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 line: Peer-review under responsibility of the VCSI1 organizers. Keywords: Fracture Mechanics; 3D e ff ects; coupled modes; stress singularities; vertex singularities; stress intensity factors 1st Virtual Conference on Structural Integrity – VCSI1 3D e ff ects on Fracture Mechanics Marco Maurizi a, ∗ , Filippo Berto a a NTNU - Norwegian University of Science and Technology –Department of Mechanical Engineering, 7491 Trondheim, Norway

Nomenclature Nomenclature

2452-3216 © 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 VCSI1 organizers 10.1016/j.prostr.2020.04.032 ∗ Corresponding author. Tel.: + 39-327-780-3296. E-mail address: marco.maurizi@ntnu.no 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 line: P er-review under responsibility of the VCSI1 organizers. x , y , z Cartesian coordinates r , θ , z cylindrical / polar coordinates σ i j i , j − th stress component 2 h plate thickness γ supplementary V-notch opening angle and crack surface intersection angle 2 α V-notch opening angle ∗ Corresponding author. Tel.: + 39-327-780-3296. E-mail address: marco.maurizi@ntnu.no 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 line: Peer-review under responsibility of the VCSI1 organizers. x , y , z Cartesian coordinates r , θ , z cylindrical / polar coordinates σ i j i , j − th stress component 2 h plate thickness γ supplementary V-notch opening angle and crack surface intersection angle 2 α V-notch opening angle