PSI - Issue 35

E.A. Dizman et al. / Procedia Structural Integrity 35 (2022) 91–97 Author name / Structural Integrity Procedia 00 (2021) 000–000

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Fig. 1: Left: Undeformed configuration Middle: Rotation of fibers with the matrix; Right: fibers stay almost fixed in their original orientation.

± 45 ◦ laminates and o ff -axis compression tests of uni-directional laminates. The nonlinear hardening is attributed to matrix yielding and in some cases, structures can sustain over 20 % strain. In composite mechanics, the constitutive laws have typically two major components, namely, a stress-strain relation and a failure criterion to predict the onset of failure, Hashin (1965), Puck and Schu¨rman (2010). Some of these models are accompanied by damage evolution laws that are used to degrade the material state. Most of these models are formulated in geometrically linear and small strain context since most of the components fail at relatively low strain levels. Experimental studies reveal that, under shear deformations, fibers do not rotate but the matrix shears typically along fiber direction. Classical plasticity models including the Hill’s original one, would impose the same rotation for the matrix and the fibers. However the rotation of the matrix and the fibers di ff er significantly as strain increases, please see Figure 1 for an illustration and Tan and Falzon (2016) for experimental evidence. This clearly shows that the kinematic description of the model shall have the capacity to describe the ‘relative rotation’. Obviously, plasticity models with plastic spin would be the proper approach to address this problem, however additional tensorial constitutive laws for plastic spin and the identification of the associated material parameters make this alternative less attractive. In fact, crystal plasticity used for metals, have the capacity to capture plastic spin and recently, researchers have started to exploit it in the context of composite inelasticity, Meza et al. (2019), Tan and Liu (2020). In order to adopt crystal plasticity to composites, it is assumed that plastic deformations are the result of matrix shearing along certain slip directions. Successful predictions of these models as compared to experimental results suggest that this approach could be a viable alternative to capture hardening behaviour and fiber rotations in a consistent manner. This paper aims at investigating the predictive capabilities of crystal plasticity inspired models for composites. To this end, the model proposed in Meza et al. (2019), Tan and Liu (2020), Tan and Falzon (2021) is formulated in an implicit setting and implemented in commercial finite element solver Abaqus through user defined element (UEL) subroutine. In the next section, adaptation of the crystal plasticity model along with the associated slip systems and hardening mechanism at slip level are addressed. In the following section stress integration and solution algorithm are briefly introduced. The capabilities of the model is investigated to a certain extent by two example problems before the paper is closed by conclusions and outlook section. Due to experimentally observed localized shear deformations of CFRP’s Gonzalez and Llorca (2007), it is assumed that plastic deformation can be described by shearing along certain slip directions. Similar to crystal plasticity, first a lattice structure is introduced which is labeled by fiber direction. With respect to local (lattice) coordinate system 1-2-3, there are six slip systems which can be categorized into two groups as longitudinal and transverse slip systems, please see Figure 2. Each of these slip systems are described by slip direction vector s α 0 and slip plane normal direction vector m α o which are given in Table 1 for α = 1 , 6. The deformation of any material point is split into plastic and elastic parts such that the shearing along slip systems constitute the plastic part which is followed by the elastic deformation and rigid body rotations. Mathematically, this is expressed by the following multiplicative split of deformation gradient F 2. Crystal Plasticity Inspired Model

F = F e F p

(1)