Session: 13-11-02: Friction, Fracture, and Damage II

Paper Number: 167997

Phase Field Modeling of Fracture in Laminated Composites 

In fracture mechanics, phase field modeling is used to represent sharp crack interfaces in a smeared manner using a suitable length scale parameter. The evolution of phase field variable (representing crack evolution) is achieved by minimizing the summation of bulk energy and crack surface energy of the solid body.

Laminated composites involve different layers of lamina stacked over each other. Each lamina contains unidirectional/bidirectional fibers embedded in a matrix. The change in direction of fibers in different lamina leads to complex crack paths in laminated composites. Such kind of crack evolution can be captured using anisotropic phase field models which either incorporate an anisotropic tensor with a single-phase field variable or multiple phase field variables or both [1] to model the fiber direction dependent crack evolution in each lamina. The interaction between the crack across adjacent laminae is modeled by employing a cohesive zone model at the laminae interfaces [2].

In order to model phase field evolution in isotropic plates, various authors have used Kirchoff plate theory for thin plates [3], and Reissner Mindlin [4] and higher order plate theory for moderately thick plates [5]. However, investigation of computational efficiency and accuracy of different plate theories to predict crack evolution in laminated composite plates using phase field approach is still an open area of research. Therefore, a detailed study on efficiency and robustness of different plate theories for phase field modeling in laminated composite plates is carried out. An open source FEniCS based finite element code is developed to model phase field evolution using First order Shear Deformation Theory (FSDT), Higher order Shear Deformation Theory (HSDT) with cubic through the thickness approximation of in-plane displacements, HSDT with Thickness stretch and Zig-zag terms (HSDTTZ) and three-dimensional finite element. Anisotropic phase field model with a single phase field variable is used to capture the crack propagation. Parametric study for different lamination schemes, boundary conditions and loading conditions is carried out to test the efficacy of different plate theories in modeling phase field evolution. The developed FEniCS based framework predicts change in crack path with change in fiber angle in a lamina consistent with the results available in literature [1]. Detailed results related to laminated composite plates will be presented in the conference.

References :

[1] Pillai U, Triantafyllou SP, Essa Y, de la Escalera FM. An anisotropic cohesive phase field model for quasi-brittle fractures in thin fibre-reinforced composites. Compos Struct 2020;252:112635. https://doi.org/10.1016/j.compstruct.2020.112635.

[2] Quintanas-Corominas A, Turon A, Reinoso J, Casoni E, Paggi M, Mayugo JA. A phase field approach enhanced with a cohesive zone model for modeling delamination induced by matrix cracking. Comput Methods Appl Mech Eng 2020;358. https://doi.org/10.1016/j.cma.2019.112618.

[3] Kiendl J, Ambati M, De Lorenzis L, Gomez H, Reali A. Phase-field description of brittle fracture in plates and shells. Comput Methods Appl Mech Eng 2016;312:374–94. https://doi.org/10.1016/j.cma.2016.09.011.

[4] Kikis G, Ambati M, De Lorenzis L, Klinkel S. Phase-field model of brittle fracture in Reissner–Mindlin plates and shells. Comput Methods Appl Mech Eng 2021;373:113490. https://doi.org/10.1016/j.cma.2020.113490.

[5] Raghu P, Rajagopal A, Reddy JN. Thermodynamically Consistent Variational Approach for Modeling Brittle Fracture in Thick Plates by a Hybrid Phase Field Model. J Appl Mech Trans ASME 2020;87:1–14. https://doi.org/10.1115/1.4045236.

Presenting Author: Shubham Rai Indian Institute of Technology Delhi

Presenting Author Biography: Mr. Shubham Rai is a Prime Minister's Research Fellow (PMRF) pursuing Ph.D. from the Department of Applied Mechanics, IIT Delhi, New Delhi, India under the supervision of Prof. B.P. Patel.

He carries a rich blend of good academics and professional experience with a B.Tech. in Mechanical Engineering (2018 batch) from J.C. Bose University of Science and Technology YMCA, Faridabad, Haryana, India. He has also worked as a Territory Service Manager, Nexa Channel, Maruti Suzuki India Ltd. in Mumbai, India.

His research interests are non-linear finite element method, continuum damage mechanics, phase field modeling of fracture, fiber reinfored composites and computational mechanics

Authors:

Shubham Rai Indian Institute of Technology Delhi
Abhinav Gupta Vanderbilt University
Badri Prasad Patel Indian Institute of Technology Delhi
Ravindra Duddu Vanderbilt University