PSI - Issue 42

Available online at www.sciencedirect.com Available online at www.sciencedirect.com ^ĐŝĞŶĐĞ ŝƌĞĐƚ Structural Integrity Procedia 00 (2019) 000 – 000 il l li t . i i t. tr t r l I t rit r i ( )

www.elsevier.com/locate/procedia . l i r. /l t / r i

ScienceDirect

Procedia Structural Integrity 42 (2022) 553–560

© 2022 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 scientific committee of the 23 European Conference on Fracture – ECF23 Abstract In the Phase Field methodology there is a length parameter related to the size of the damage region, which is proportional to the Irwin length. In this work, we apply the Phase Field methodology to the analysis of fracture at the micro-scale in brittle materials, studying the role of this length parameter when the size of the specimen is of the order of the Irwin length. We compare the conclusions obtained with the ones previously presented using Finite Fracture Mechanics. Two different schemes are used, a staggered and a monolithic scheme. © 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 23 European Conference on Fracture - ECF23 Keywords: Micro-scale – Fracture properties – Phase Field – Brittle fracture 1. Main text One of the fundamental ingredients of the recent methodology Finite Fracture Mechanics (FFM) for the prediction of crack events in materials and structures, is that a crack is assumed to jump a given finite length at onset. This can be formulated through the invocation of the Coupled Criterion (CC) presented in Leguillon (2002), stating that this length depends on the material toughness, the tensile strength but also the geometry. Complying with a different vision, according to Pham et al. (2011) and Bourdin et al. (2014), in the Phase Field (PF) of fracture, there exist a material related length that describes the size of the damaged region, called the phase field length scale. Both the PF length scale and the nucleation length obtained by the CC are proportional to the Irwin length defined from the material toughness and the tensile strength. At the macro-scale, they are small compared to any dimension of the structure, t i l t l t i l t t l t t t i t i , i i ti l t t i l t . t i , l t i l t l t t l i t t t i l i ittl t i l , t i t l t i l t t t i t i i t t i l t . t l i t i it t i l t i i it t i . i t , t lit i . t . li l i . . This is an ope ti l t li tt :// ti . /li / / . / i i ilit t : i r - l r t r r rti i l rittl fr t r . i t t l i i t t t t l i it t i t i ti t i t i l t t , i t t i t j i i it l t t t. i l t t t i ti t l it i t i ill , t ti t t t i l t t t i l t , t t il t t t l t t . l i it i t i i , i t t l. i t l. , i t i l t , t i t t i l l t l t t t i t i t i , ll t i l l t l . t t l t l t l ti l t t i t ti l t t i l t i t t i l t t t il t t . t t l , t ll t i i t t t , 23 European Conference on Fracture - ECF23 Finite Fracture Mechanics from the macro- to the micro-scale. Comparison with the Phase Field model. S. Jiménez-Alfaro a , J. Reinoso b , D. Leguillon a , C. Maurini a a Institut Jean Le Rond d’Alembert, Sorbonne Université – CNRS UMR 7190, 4 Place Juisseu, 75005, Paris, France b Grupo de Elasticidad y Resistencia de Materiales, Escuela Técnica Superior de Ingenieria de Sevilla, Universidad de Sevilla , Camino de los Descubrimientos, 41092, Sevilla, Spain S. Jimén b a I tit t ’ l t, i it , l i , , i , b l ti i i t i t i l , l i i I i i ill , i i ill , i l i i t , , ill , i

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 23 European Conference on Fracture - ECF23 l i r . . i i rti l r t - - li ( tt :// r ti . r /li / - - / . /) i i ilit t - t r . li

2452-3216 © 2022 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 scientific committee of the 23 European Conference on Fracture – ECF23 10.1016/j.prostr.2022.12.070