An anisotropic nonlinear multiscale damage model for mechanical behavior of a composite laminate with matrix cracks

The first observed damage in a composite laminate is the matrix cracks. Although not leading to rupture, these cracks reduce the equivalent mechanical properties, leading to nonlinear stress-strain behavior. Because of the crack shielding effect (CSE), damage progression and stiffness reduction are nonlinear. Talreja has introduced an effective damage method for laminates with matrix cracks, and Singh has proposed a nonlinear model based on the method to assess stiffness reduction considering the CSE. But as Singh claimed, the model suffers from errors not addressed yet. This paper explains why Singh's model has such limitations and presents a new anisotropic nonlinear multiscale damage model based on Talreja's method. The model combines macro-scale continuum damage mechanics (CDM) with finite-element (FE) micromechanics. A glass/epoxy cross-ply laminate under tension is chosen as the case study, a light-transmission experiment is conducted to specify the damage progression, and an energy-based model is used to characterize it. As Talreja's method suggests, a new function is proposed for the Helmholtz free energy, and the equations of mechanical properties in terms of the crack density are derived. FE micromechanical models with periodic boundary conditions (PBC) are developed to determine the damage constants. The model is then applied to predict the stress-strain diagram of the laminate, the results are validated by tensile and loading-unloading experiments, and compared with Singh and Talreja's models. Also, reference state selection criteria are established for the new model to obtain the best predictions, which was impossible with Singh's model.

Automated summary

This paper presents a new anisotropic nonlinear multiscale damage model based on Talreja's method to predict the stress-strain behavior of composite laminates. By conducting a light-transmission experiment and using finite-element micromechanics, the relationship between damage progression, mechanical properties equations, and crack density is determined. The model is validated and compared with existing models, and reference state selection criteria are established for optimal predictions.