PSI - Issue 21

Available online at www.sciencedirect.com

Available online at www.sciencedirect.com Available online at www.sciencedirect.com

ScienceDirect Structural Integrity Procedia 00 (2019) 000–000 Structural Integrity Procedia 00 (2019) 000–000 Procedia Structural Integrity 21 (2019) 52–60

www.elsevier.com / locate / procedia

www.elsevier.com / locate / procedia

1st International Workshop on Plasticity, Damage and Fracture of Engineering Materials Development of a Micromechanics Based Cohesive Zone Model and Application for Ductile Fracture 1st International Workshop on Plasticity, Damage and Fracture of Engineering Materials Development of a Micromechanics Based Cohesive Zone Model and Application for Ductile Fracture

Tuncay Yalc¸inkaya a, ∗ , Izzet Tarik Tandogan a , Alan Cocks b a Department of Aerospace Engineering, Middle East Technical University, Ankara 06800, Turkey b Department of Engineering Science, University of Oxford, Parks Road, Oxford, OX1 3PJ, UK Tuncay Yalc¸inkaya a, ∗ , Izzet Tarik Tandogan a , Alan Cocks b a Department of Aerospace Engineering, Middle East Technical University, Ankara 06800, Turkey b Department of Engineering Science, University of Oxford, Parks Road, Oxford, OX1 3PJ, UK

2452-3216 © 2019 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 1st International Workshop on Plasticity, Damage and Fracture of Engineering Materials organizers 10.1016/j.prostr.2019.12.086 ∗ Corresponding author. Tel.: + 90 312 2104258 ; fax: + 90 312 2104250. E-mail address: yalcinka@metu.edu.tr 2210-7843 c ⃝ 2019 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 1st International Workshop on Plasticity, Damage and Fracture of Engineering Materials organizers. 1. Introducti n It has been more than fifty years since the first appearence of the cohesive zone concept by Barenblatt (1959) and Dugdale (1960). After the pioneering work of Hillerborg et al. (1976), over the years, it has been proven to be powerful in modeling of fragmentation of materials when coupled with the finite element method. With this approach the fracture mechanism is represented with interface elements placed in-between the bulk elements at the locations of potential separation. These interface elements are able to open up similar to a crack, and their behaviour is governed by the traction-separation law while the bulk elements remain undamaged. The maximum traction, the area under the traction-separation curve, and the critical separation where the traction becomes zero are the main characteristics of such laws. Cohesive zone modelling has been one of the most popular approaches for modelling fracture process, yet it is mostly based on phenomenological relations and do not consider the physics at the fracture process zone. Hence, ∗ Corresponding author. Tel.: + 90 312 2104258 ; fax: + 90 312 2104250. E-mail address: yalcinka@metu.edu.tr 2210-7843 c ⃝ 2019 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 1st International Workshop on Plasticity, Damage and Fracture of Engineering Materials organizers. © 2019 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 1st International Workshop on Plasticity, Damage and Fracture of Engineering Materials organizers Abstract In this paper, derivation and implementation of a micromechanically motivated traction separation law for cohesive zone model ing of ductile fracture is discussed. The formulation of the framework is based on the growth of pores in an array of representative volume elements where pores are idealized as cylinders. Two relations are derived under normal and shear loading for mode-I and mixed-mode respectively, based on the upper bound for a perfectly plastic material (Yalcinkaya and Cocks (2015), Yalc¸inkaya and Cocks (2016)). The obtained traction-separation laws are used as the constitutive model for cohesive elements. Numerical simulations are conducted for a compact tension specimen to illustrate the performance of the model under mode-I loading where the e ff ect of the size and the shape of the pores are illustrated explicitly. It was observed that increasing initial pore fraction or decreasing initial pore height has a detrimental e ff ect on the material, which decreases the strength and the toughness as expected. c ⃝ 2019 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 1st Internati nal Workshop on Plasticity, Damage and Fracture of Engineering Materials organizers. Keywords: cohesive zone model; ductile fracture; porous plasticity 1. Introduction It has been more than fifty years since the first appearence of the cohesive zone concept by Barenblatt (1959) and Dugdale (1960). After the pioneering work of Hillerborg et al. (1976), over the years, it has been proven to be powerful in modeling of fragmentation of materials when coupled with the finite element method. With this approach the fracture mechanism is represented with interface elements placed in-between the bulk elements at the locations of potential separation. These interface elements are able to open up similar to a crack, and their behaviour is governed by the traction-separation law while the bulk elements remain undamaged. The maximum traction, the area under the traction-separation curve, and the critical separation where the traction becomes zero are the main characteristics of such laws. Cohesive zone modelling has been one of the most popular approaches for modelling fracture process, yet it is mostly based on phenomenological relations and do not consider the physics at the fracture process zone. Hence, Abstract In this paper, derivation and implementation of a micromechanically motivated traction separation law for cohesive zone odel ing of ductile fracture is discussed. The formulation of the framework is based on the growth of pores in an array of representative volume elements where pores are idealized as cylinders. Two relations are derived under normal and shear loading for mode-I and mixed-mode respectively, based on the upper bound for a perfectly plastic material (Yalcinkaya and Cocks (2015), Yalc¸inkaya and Cocks (2016)). The obtained traction-separation laws are used as the constitutive model for cohesive elements. Numerical simulations are conducted for a compact tension specimen to illustrate the performance of the model under mode-I loading where the e ff ect of the size and the shape of the pores are illustrated explicitly. It was observed that increasing initial pore fraction or decreasing initial pore height has a detrimental e ff ect on the material, which decreases the strength and the toughness as expected. c ⃝ 2019 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 1st International Workshop on Plasticity, Damage and Fracture of Engineering Materials organizers. Keywords: cohesive zone model; ductile fracture; porous plasticity