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• The ply-by-ply shell layer model for laminates with gaps is developed. • The gap is modeled by the extended finite element method and cohesive zone model. • The same mesh is applicable for the hole and gaps of various geometries. • The open hole tensile analysis is performed on a laminate with gaps. • The overall load–strain behavior up to failure agrees well with the experiment. Although automated fiber placement manufacturing can improve productivity, gaps and overlaps of plies occur due to the low position accuracy of the robot arm. This study develops the ply-by-ply shell layer model to investigate the mechanical effects of a gap on the damage progression and strength of composite laminates with a hole. The gaps and a hole are modeled independently of the mesh using the extended finite element method (XFEM) to reduce the preprocessing and computational costs using a simple square mesh. The opening of the resin rich area of the gap is represented by applying the cohesive zone model to the crack surface. The open hole tensile analysis was performed on a laminate with gaps. The predicted strength of specimen with gaps agrees well with the experiment and is slightly higher than that of specimen without gaps because the gap opening reduces the stress concentration at the hole. [ABSTRACT FROM AUTHOR]

In this study, the continuum damage mechanics model for predicting the stiffness reduction of composite laminates including transverse cracks is formulated as a function of crack density. To formulate the model, first the damage variable in the direction normal to the fiber of a ply including transverse cracks is derived. The damage variable is derived by the model assuming a plane strain field in the isotropic plane and using the Gudmundson–Zang model for comparison. The effective compliance based on the strain equivalent principle proposed by Murakami et al. and classical laminate theory are then used to formulate the elastic moduli of laminates of arbitrary lay-up configurations as a function of the damage variable. Finally, the results obtained from this model are compared to the finite-element analysis reported in previous studies. The model proposed in this paper can predict the stiffness of laminates containing damage due to transverse cracks (or surface crack) from just the mechanical properties of a ply and the lay-up configurations. Furthermore, this model can precisely predict the finite-element analysis results and experiment results for the elastic moduli of the laminate of arbitrary lay-up configuration, such as cross-ply, angle ply, and quasi-isotropic, including transverse cracks. This model only considers the damage of the transverse crack; it does not consider damage such as delamination. However, this model seems to be effective in the early stage of damage formation when transverse cracking mainly occurs. The model assuming plane strain field in the isotropic plane which is proposed in this paper can calculate the local stress distribution in a ply including transverse cracks as a function of crack density. The damage evolution of transverse cracks can thus be simulated by determining the fracture criterion. [ABSTRACT FROM AUTHOR]

• We develop an analytical 3D effective compliance of laminates with ply cracks. • Two damage parameters are formulated analytically as functions of ply crack density. • A steady-state laminate cracking analysis model is established. • The proposed model considers the effect of damage due to internal or surface cracks. • The proposed model can reproduce the numerical and experiment results. An analytical three-dimensional effective elastic constant of transversely isotropic plates that include ply cracks is proposed using a continuum damage mechanics approach. Two damage parameters associated with tensile and shear damage are formulated as functions of ply crack density using local stress fields that satisfy the equilibrium equations. Three-dimensional laminate theory is then employed to formulate the effective compliance of the laminate using the effective compliance of a damaged ply, and an analytical steady-state cracking model is established. The proposed model reproduces the thermomechanical properties and the crack initiation stress of laminates. [ABSTRACT FROM AUTHOR]