Theoretical and Applied Fracture Mechanics xxx (xxxx) xxx Please cite this article as: Carlos Esteves, Theoretical and Applied Fracture Mechanics, https://doi.org/10.1016/j.tafmec.2022.103668 Available online 11 November 2022 0167-8442/© 2022 Elsevier Ltd. All rights reserved. A 2D numerical modelling of plasticity induced crack closure on MT specimens Carlos Esteves a , Daniel F.O. Braga b , Behzad V. Farahani b, * , Pedro M.G.P. Moreira b , Ricardo Baptista a, c, * , Virginia Infante a a IDMEC, Instituto Superior T´ ecnico, Universidade de Lisboa, Av. Rovisco Pais, 1049-001 Lisboa, Portugal b INEGI, Faculty of Engineering, University of Porto, Dr. Roberto Frias Street, N 400, 4200-465 Porto, Portugal c CDP2T, Escola Superior de Tecnologia de Setúbal, Instituto Polit´ ecnico de Setúbal, Setúbal 2910-761, Portugal A R T I C L E INFO Keywords: Fatigue cracks Stress intensity factor FEM Crack closure Fracture mechanics ABSTRACT In many engineering felds, structures are often subjected to fatigue loading that initiate and propagate cracks. The development of fracture mechanics studies has enabled the tolerance of a substantial amount of damage and the ability to predict failure in fatigue damaged structures, extending their service life safely. This can bring social impacts from economics, public-safety, or an environmental point of view. These damage tolerance an- alyses can be performed using linear elastic fracture mechanics (LEFM), where the Stress Intensity Factor (SIF) is a chief key, or under elastoplastic fracture mechanics (EPFM), where plasticity induced crack closure (PICC) plays a major role on fatigue crack growth (FCG). This study deals with the computational modelling developed consisting in the simulation of a two-dimensional model to predict FCG under PICC conditions. Extremely fne meshes were generated around the crack tip, in order to predict PICC loads, SIF and plastic zone size. The results showed good agreement with the experimental model, allowing for accurate damage tolerance assessments. 1. Introduction Fracture mechanics, in conjunction with fatigue crack growth laws, are extensively used to predict and analyse the fracture behaviour of engineering structures. Rigorous analyses must be implemented to ac- quire fracture parameters including the stress intensity factor (SIF) to access the remaining life of a certain structural component. Neverthe- less, in-service structures can suffer damage propagation, which changes their initial stress state and may lead to the presence of fatigue cracks. The knowledge of the deformation variation adjacent to a fatigue crack tip can contribute to an existent determination of a structural health, allowing cost reduction through programmed interventions, while still ensuring safety [1]. The existence of cracks in structures or components subjected to fatigue loads stimulates the necessity to measure, study and predict their propagation, the stress feld around it and its consequences in the structure life span. A better knowledge of these felds can bring im- provements in different felds of engineering, from design to inspection, monitoring, and product maintenance. Beside these, other advantages can accrue from technological evolution such as better evaluation of safety measures and less material waste, which result in economic and environmental gains. The advances made so far in this area are responsible, from many other things, for the increase in airplane’s fuselage lifespan and other transportation components, for the improvement of medical prosthesis, or the control of larger structures stress areas such as rivets in metallic bridges. For more than fve decades, the fnite element method (FEM) has been used to analyse and study the plasticity induced crack closure (PICC) phenomenon [2]. Even though other mechanisms have been used to explain crack closure, PICC is considered as the most important methodology. Due to fatigue crack growth (FCG), the yielded material around the crack tip causes premature contact of the crack fanks, even if a tensile load is still remotely applied. This matter is explained by the large tensile plastic strains that progress ahead of the crack tip, not fully reversed during the subsequent fatigue cycles, resulting in the formation of a plastic wake behind the crack tip. Therefore, FCG will be delayed by the reduced crack growth rate [3]. More recent progress in the crack closure effects can be found in the following papers [4–7]. The stress intensity level at which Mode I opening load occurs, K op , will then defne an effective SIF range causing fatigue,ΔK eff = K max K op = UΔK. Where U defnes the crack closure ratio U = * Corresponding authors. E-mail addresses: bfarahani@inegi.up.pt (B.V. Farahani), ricardo.baptista@estsetubal.ips.pt (R. Baptista). Contents lists available at ScienceDirect Theoretical and Applied Fracture Mechanics journal homepage: www.elsevier.com/locate/tafmec https://doi.org/10.1016/j.tafmec.2022.103668 Received 7 September 2022; Received in revised form 16 September 2022; Accepted 5 November 2022