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type:Research Article, Lamb wave propagation must be understood comprehensively for simply evaluating delamination during ultrasonic testing. However, the difference between wave propagation, visualized using laser Doppler vibrometer and pulsed-laser scanners, has not been sufficiently investigated, and knowledge of optimal conditions for evaluating delamination is limited. Thus, in this study, the mode conversion and multiple reflections of Lamb waves propagating in a delaminated cross-ply laminate were visualized using different laser scanners, delamination depths, and wave incident angles. Delamination was characterized using maximum-amplitude map postprocessing under specific conditions. Further numerical analysis revealed that owing to multiple reflections of the antisymmetric mode in incident and mode-converted waves, standing waves were generated in the delaminated sublaminate. Dispersion curve and flexural stiffness calculations confirmed the conditions required for high-amplitude standing waves, thereby providing guidelines for simply and reliably evaluating delamination during inspections.

type:Research Article, In this study, a model for the three-dimensional effective compliance of composite laminates with transverse cracks is developed based on continuum damage mechanics. Three-dimensional laminate theory is used to reproduce all the thermoelastic properties of the damaged laminate. The damage variable, which describes the degree of stiffness reduction caused by transverse cracking, is formulated based on a three-dimensional micromechanical model, with a loose boundary condition and assuming parabolic crack opening. These assumptions contribute to the analytical accuracy of the stiffness reduction model, while simplifying the damage variable expression. The effective thermomechanical properties of various composite laminates are predicted using the proposed model and compared with finite element analysis (FEA) and experimental results. We found that the proposed model with derived damage variable successfully reproduces the FEA and experimental results of stiffness degradation of damaged composite laminates.

type:Articles, This study predicted transverse cracking progression in laminates including 90° plies. The refined stress field (RSF) model, which takes into account thermal residual strain for plies including transverse cracks is formulated, and the energy release rate associated with transverse cracking is calculated using this model. For comparison, the energy release rate based on the continuum damage mechanics (CDM) model is formulated. Next, transverse cracking progression in CFRP cross-ply laminates including 90° plies is predicted based on both stress and energy criteria using the Monte Carlo method. The results indicated that the RSF model and the CDM model proposed in this study can predict the experiment results for the relationship between transverse crack density and ply strain in 90° ply. The models presented in this paper can be applied to an arbitrary laminate including 90° plies.

In this study, the continuum damage mechanics model for predicting the stiffness re duction 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 vari able 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 and his colleagues 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 (FEA) 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 FEA 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, includ ing 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 oc curs. 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.

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 variables 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.

The present paper proposes a new analytical model for predicting the effective stiffness of composite laminates with fiber breaks and transverse cracks. The model is based on continuum damage mechanics and the classical laminate theory. We derived damage variables describing stiffness reduction due to fiber breaks and its maximum value during ultimate tensile failure from the global load-sharing model. Furthermore, a simplified analytical model is presented for obtaining two damage variables for a cracked ply subjected to transverse tensile loading or in-plane shear loading. This model was developed assuming that the displacement field of the longitudinal direction can be expressed in the form of a quadric function by loosening the boundary condition for the governing differential equation. For verifying the developed model, the elastic constants of damaged composite laminates were predicted for cross-ply and angle-ply laminates and compared with finite element analysis results. As for the appropriate expression of the effective elastic stiffness matrix of the damaged ply, we verified four types of effective compliance/stiffness matrices including the Murakami, Yoshimura, Li and Maim´ı models. We found the Maim´ı model to be the most appropriate among these four models. Moreover, we successfully simplified the expressions for damage variables in the complicated infinite series obtained in our previous study.We also proved that this could contribute toward improving the accuracy of our analysis. After verifying the present model, the stress-strain response and failure strength of carbon- or glass- fiber-reinforced plastic cross-ply laminates were predicted using Maim´ı’s compliance model and the simplified damage variables.

A multiscale approach comprising laminate-scale finite-element (FE) analysis and fiber-diameter-scale periodic unit cell (PUC) analysis was developed to predict matrix microcracking in quasiisotropic laminates; further, this method was validated through comparison of our predictions with experimental results. In the mesoscopic FE analysis, the nonlinear deformation in the unidirectional laminae was incorporated to reproduce the deformation behavior of the laminate and obtain deformation histories at the locations of expected crack initiation in the laminate. In the microscopic analysis, the nonlinear behavior and crack initiation in the matrix resin were simply modeled by an elasto-viscoplastic law and a stress-based failure criterion, respectively. To predict crack initiation considering both the macroscopic deformation fields and the microscopic heterogeneity of the material, the mesoscopic FE analysis was conducted first. Subsequently, the microscopic PUC analysis was undertaken based on the strain histories obtained from the mesoscopic analysis. Our multiscale approach was applied to quasi-isotropic laminates with several laminate configurations to predict the matrix cracks in the 90° ply of the laminates. In addition to referring to experimental data cited in literature, initial and transverse cracks were observed when conducting tensile tests of quasi-isotropic laminates using the in situ replication technique and ex situ X-ray computed tomography. Through comparison of the predicted values with experimental results quoted in literature and obtained in this work,we validated the prediction capability of our multiscale analysis and evaluated the process of crack formation from the mesoscopic and microscopic points of view. Moreover, we examined the sensitivity of predicted results to fiber arrangement and the influence of constitutive and failure modeling of two-scale analysis on predicted cracking strains. The reported method can predict initial and transverse