Interaction of anisotropic crack phase field with interface cohesive zone model for fiber reinforced composites D. Pranavi a , A. Rajagopal a,⇑ , J.N. Reddy b a Indian Institute of Technology Hyderabad, Telangana, India b Texas A&M University, College Station, Texas, United States ARTICLE INFO Keywords: Composites Anisotropic crack Phase field Cohesive zone model Interface crack interaction ABSTRACT A new phase field model considering the interfacial damage for different configurations of a fiber reinforced composite is proposed and formulated. Crack and non local interface are considered to be diffused. A coupled traction separation law based on a potential function is adopted to represent the behavior of the interface. Anisotropy is introduced into the elastic equilibrium by considering the distinct contributions of fiber and matrix in different modes. The present model captures the predominant failure phenomena in a composite such as matrix failure, delamination by considering the role of fiber orientation, interface fracture properties and configuration of lamina. The proposed formulation is extended to a fiber reinforced composite lamina consist- ing of two fiber families oriented in different directions. Parametric studies are conducted to understand the effect of anisotropy parameter, length scales, fracture properties of fiber, matrix and interface on crack prop- agation and mechanical response of the whole system. Numerical examples are performed to validate the pro- posed model, understand the anisotropic crack growth for unidirectional and woven fiber reinforced composites, study the interaction of anisotropic crack with composite‐composite interface and metal‐ composite interface. 1. Introduction Fiber reinforced composites (FRCs) are used widely in several important industrial applications. To enable efficient design of such composites, it is important to understand the complex failure mecha- nisms in such materials [1]. The anisotropic material behavior of FRCs makes it more complex to model. The properties of different con- stituent phases namely fiber, matrix, fiber–matrix interface together with stacking sequence and thickness of the laminate decides the over- all properties of such composites. Interaction of the interfaces is a cru- cial factor in determining the overall strength of the composite [2]. Failure modes of a laminated fiber‐reinforced composite at mesos- cale can be distinguished broadly into: (a)Intralaminar, failure within the lamina like matrix cracking or fiber breakage; (b)Interlaminar, fail- ure between the laminae like delamination; and (c)Translaminar, fail- ure along the laminate thickness, as shown in Fig. 1 [3]. Understanding the structural integrity of composites requires develop- ing robust damage models to predict critical fracture strength and the complex anisotropic crack propagation accurately. Several methods have been proposed in the literature, notable among these includes: anisotropic continuum damage models to predict the intralaminar fracture by conducting studies on open hole test specimens [4], and by adopting 3D puck failure theory [5], finite fracture mechanics based model [6] where the fiber–matrix interface debonding is studied using cohesive zone model, fracture models based on XFEM (see [7,8]) to understand the failure phenomena in composites with single and multi fibers, floating point methods [9], cohesive zone models to ana- lyze the deflection and penetration events when there is a crack‐ interface interaction (see [10,11]) in polycrystalline materials [12], and non local gradient damage models (see [13,14]). A damage model has been developed to simulate delamination under different modes of loading [15]. More recently, the phase field model (PFM) has been developed using variational approaches [16]. This enables the simulation of com- plex fracture phenomena involving crack branching and crack merg- ing. The variational problem is minimized to obtain the coupled equilibrium and evolution equations, which are solved in a staggered approach (see [17,18]). Quasi‐static phase‐field formulation has been implemented for modeling brittle fracture (see [19,20]), ductile frac- ture (see [21,22]). This approach has also been applied for dynamic https://doi.org/10.1016/j.compstruct.2021.114038 Received 20 February 2021; Revised 25 April 2021; Accepted 28 April 2021 Available online 6 May 2021 0263-8223/© 2021 Elsevier Ltd. All rights reserved. ⇑ Corresponding author. E-mail address: rajagopal@ce.iith.ac.in (A. Rajagopal). Composite Structures 270 (2021) 114038 Contents lists available at ScienceDirect Composite Structures journal homepage: www.elsevier.com/locate/compstruct